WorldWideScience

Sample records for monoclinic space-group symmetry

  1. A Phase Transformation with no Change in Space Group Symmetry: Octafluoronaphtalene

    DEFF Research Database (Denmark)

    Pawley, G. S.; Dietrich, O. W.

    1975-01-01

    A solid-state phase transformation in octafluoronaphthalene has been discovered at 266.5K on cooling, and at 15K higher on heating. The symmetry of both phases is found to be the same, namely monoclinic with space group P21/c. The unit cell parameters change by up to 10%, but the integrity...... of a single crystal, which shatters on cooling, is good enough for a single-crystal structure determination. This has been done in both phases to a sufficient accuracy that a mechanism for the transformation can be proposed. Molecules which lie parallel to one another shear to a new parallel position...

  2. Crystallite size effect on the monoclinic deformation of the bcc crystal structure of chromium

    Science.gov (United States)

    Przeniosło, R.; Fabrykiewicz, P.; Sosnowska, I.; Wardecki, D.; Sławiński, W. A.; Playford, H. Y.; Hempelmann, R.; Bukowski, M.

    2018-02-01

    The modulated spin density wave magnetic orderings observed in chromium suggests that the crystal structure of chromium cannot be described by the cubic space group Im 3 bar m. Our experimental studies of polycrystalline and nanocrystalline chromium by synchrotron radiation (SR) and neutron powder diffraction show a hkl-dependent Bragg peak broadening which can be interpreted by the low-symmetry monoclinic space group P21 / n instead of the high symmetry cubic space group Im 3 bar m. The monoclinic angle is βm = 90.05(1)° and 90.29(1)° for polycrystalline Cr and nanocrystalline Cr, respectively. The relative monoclinic distortion observed in chromium is 5 times larger than those reported for several oxides: BiFeO3, α-Fe2O3, Cr2O3 and calcite. The symmetry of the magnetic transverse spin density wave (TSDW) and the longitudinal spin density wave (LSDW) observed in Cr are described by using the superspace groups P21 / n(0 β 0) 00 and P 21‧ /n‧(0 β 0) 00, respectively. These superspace groups describe both the magnetic modulations and the atomic position modulations reported in the literature. The monoclinic symmetry of chromium is a robust effect which is observed in the paramagnetic as well as in the TSDW and LSDW phases.

  3. Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in ZrO2

    Science.gov (United States)

    Thomas, John C.; Van der Ven, Anton

    2017-10-01

    Group/subgroup structural phase transitions are exploited in a wide variety of technologies, including those that rely on shape-memory behavior and on transformation toughening. Here, we introduce an approach to identify symmetry-adapted strain and shuffle order parameters for any group/subgroup structural transition between a high-symmetry parent phase and its symmetrically equivalent low-symmetry product phases. We show that symmetry-adapted atomic shuffle order parameters can be determined by the diagonalization of an orbital covariance matrix, formed by taking the covariance among the atomic displacement vectors of all symmetrically equivalent product phase variants. We use this approach to analyze the technologically important tetragonal to monoclinic structural phase transformation of ZrO2. We explore the energy landscapes, as calculated with density functional theory, along distinct paths that connect m ZrO2 to t ZrO2 and to other m ZrO2 variants. The calculations indicate favorable pairs of variants and reveal intermediate structures likely to exist at coherent twin boundaries and having relatively low deformation energy. We identify crystallographic features of the monoclinic ZrO2 variant that make it very sensitive to shape changing strains.

  4. The monoclinic polymorph of dimethylarsinic acid

    Directory of Open Access Journals (Sweden)

    Richard Betz

    2011-08-01

    Full Text Available The title compound, C2H7AsO2 or [As(CH32O(OH], is an organic derivative of arsinic acid, and is also known by its trivial name cacodylic acid. In contrast to the first polymorph (triclinic, space group Poverline{1}, Z = 2, the current study revealed monoclinic symmetry (space group C2/c, Z = 8 for the second polymorph. The configuration of the tetrahedral molecule shows approximate Cs symmetry. Strong O—H...O hydrogen bonds connect the molecules to infinite zigzag chains along [010], which are further connected by weak intermolecular C—H...O contacts into a three-dimensional network.

  5. Effects of monoclinic symmetry on the properties of biaxial liquid crystals

    Science.gov (United States)

    Solodkov, Nikita V.; Nagaraj, Mamatha; Jones, J. Cliff

    2018-04-01

    Tilted smectic liquid crystal phases such as the smectic-C phase seen in calamitic liquid crystals are usually treated using the assumption of biaxial orthorhombic symmetry. However, the smectic-C phase has monoclinic symmetry, thereby allowing disassociation of the principal optic and dielectric axes based on symmetry and invariance principles. This is demonstrated here by comparing optical and dielectric measurements for two materials with highly first-order direct transitions from nematic to smectic-C phases. The results show a high difference between the orientations of the principal axes sets, which is interpreted as the existence of two distinct cone angles for optical and dielectric frequencies. Both materials exhibit an increasing degree of monoclinic behavior with decreasing temperature. Due to fast switching speeds, ferroelectric smectic-C* materials are important for fast modulators and LCoS devices, where the dielectric biaxiality influences device operation.

  6. Broken symmetry within crystallographic super-spaces: structural and dynamical aspects

    International Nuclear Information System (INIS)

    Mariette, Celine

    2013-01-01

    Aperiodic crystals have the property to possess long range order without translational symmetry. These crystals are described within the formalism of super-space crystallography. In this manuscript, we will focus on symmetry breaking which take place in such crystallographic super-space groups, considering the prototype family of n-alkane/urea. Studies performed by X-ray diffraction using synchrotron sources reveal multiple structural solutions implying or not changes of the dimension of the super-space. Once the characterization of the order parameter and of the symmetry breaking is done, we present the critical pre-transitional phenomena associated to phase transitions of group/subgroup types. Coherent neutron scattering and inelastic X-ray scattering allow a dynamical analysis of different kind of excitations in these materials (phonons, phasons). The inclusion compounds with short guest molecules (alkane C n H 2n+2 , n varying from 7 to 13) show at room temperature unidimensional 'liquid-like' phases. The dynamical disorder along the incommensurate direction of these materials generates new structural solutions at low temperature (inter-modulated monoclinic composite, commensurate lock-in). (author) [fr

  7. Symmetry and group theory in chemistry

    CERN Document Server

    Ladd, M

    1998-01-01

    A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries.Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetryCovers both point-group and space-group symmetriesIncludes tutorial solutions

  8. Structure of bayerite-based lithium-aluminum layered double hydroxides (LDHs): observation of monoclinic symmetry.

    Science.gov (United States)

    Britto, Sylvia; Kamath, P Vishnu

    2009-12-21

    The double hydroxides of Li with Al, obtained by the imbibition of Li salts into bayerite and gibbsite-Al(OH)(3), are not different polytypes of the same symmetry but actually crystallize in two different symmetries. The bayerite-derived double hydroxides crystallize with monoclinic symmetry, while the gibbsite-derived hydroxides crystallize with hexagonal symmetry. Successive metal hydroxide layers in the bayerite-derived LDHs are translated by the vector ( approximately -1/3, 0, 1) with respect to each other. The exigency of hydrogen bonding drives the intercalated Cl(-) ion to a site with 2-fold coordination, whereas the intercalated water occupies a site with 6-fold coordination having a pseudotrigonal prismatic symmetry. The nonideal nature of the interlayer sites has implications for the observed selectivity of Li-Al LDHs toward anions of different symmetries.

  9. Reflection of P and SV waves at the free surface of a monoclinic ...

    Indian Academy of Sciences (India)

    R.Narasimhan(krishtel emaging)1461 1996 Oct 15 13:05:22

    The propagation of plane waves in an anisotropic elastic medium possessing monoclinic symmetry is discussed. The expressions for ... Keywords. Anisotropic medium; elastic waves; monoclinic half-space; reflection coefficients. Proc. Indian Acad. Sci. ...... In contrast, for C < 0, the angle of reflec- tion is less than the angle of ...

  10. Validation of missed space-group symmetry in X-ray powder diffraction structures with dispersion-corrected density functional theory

    DEFF Research Database (Denmark)

    Hempler, Daniela; Schmidt, Martin U.; Van De Streek, Jacco

    2017-01-01

    More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic...... with missed symmetry were investigated by dispersion-corrected density functional theory. In 98.5% of the cases the correct space group is found....

  11. Generation of symmetry coordinates for crystals using multiplier representations of the space groups

    DEFF Research Database (Denmark)

    Hansen, Flemming Yssing

    1978-01-01

    Symmetry coordinates play an important role in the normal-mode calculations of crystals. It is therefore of great importance to have a general method, which may be applied for any crystal at any wave vector, to generate these. The multiplier representations of the space groups as given by Kovalev...... and the projection-operator technique provide a basis for such a method. The method is illustrated for the nonsymmorphic D36 space group, and the theoretical background for the representations of space groups in general is reviewed and illustrated on the example above. It is desirable to perform the projection...... of symmetry coordinates in such a way that they may be used for as many wave vectors as possible. We discuss how to achieve this goal. The detailed illustrations should make it simple to apply the theory in any other case....

  12. Validation of missed space-group symmetry in X-ray powder diffraction structures with dispersion-corrected density functional theory.

    Science.gov (United States)

    Hempler, Daniela; Schmidt, Martin U; van de Streek, Jacco

    2017-08-01

    More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic coordinates of all non-H atoms is established to be 0.2 Å. For 98.5% of 200 molecular crystal structures published with missed symmetry, the correct space group is identified; there are no false positives. Very small, very symmetrical molecules can end up in artificially high space groups upon energy minimization, although this is easily detected through visual inspection. If the space group of a crystal structure determined from powder diffraction data is ambiguous, energy minimization with DFT-D provides a fast and reliable method to select the correct space group.

  13. A monoclinic polymorph of (1E,5E)-1,5-bis-(2-hy-droxy-benzyl-idene)thio-carbono-hydrazide.

    Science.gov (United States)

    Schmitt, Bonell; Gerber, Thomas; Hosten, Eric; Betz, Richard

    2011-08-01

    The title compound, C(15)H(14)N(4)O(2)S, is a derivative of thio-ureadihydrazide. In contrast to the previously reported polymorph (ortho-rhom-bic, space group Pbca, Z = 8), the current study revealed monoclinic symmetry (space group P2(1)/n, Z = 4). The mol-ecule shows non-crystallographic C(2) as well as approximate C(s) symmetry. Intra-molecular bifurcated O-H⋯(N,S) hydrogen bonds, are present. In the crystal, inter-molecular N-H⋯S hydrogen bonds and C-H⋯π contacts connect the mol-ecules into undulating chains along the b axis. The shortest centroid-centroid distance between two aromatic systems is 4.5285 (12) Å.

  14. Is space-time symmetry a suitable generalization of parity-time symmetry?

    International Nuclear Information System (INIS)

    Amore, Paolo; Fernández, Francisco M.; Garcia, Javier

    2014-01-01

    We discuss space-time symmetric Hamiltonian operators of the form H=H 0 +igH ′ , where H 0 is Hermitian and g real. H 0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G ′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g>0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries. - Highlights: • Space-time symmetry is a generalization of PT symmetry. • The eigenvalues of a space-time Hamiltonian are either real or appear as pairs of complex conjugate numbers. • In some cases all the eigenvalues are real for some values of a potential-strength parameter g. • At some value of g space-time symmetry is broken and complex eigenvalues appear. • Some multidimensional oscillators exhibit broken space-time symmetry for all values of g

  15. Fourier-space TEM reconstructions with symmetry adapted functions for all rotational point groups.

    Science.gov (United States)

    Trapani, Stefano; Navaza, Jorge

    2013-05-01

    A general-purpose and simple expression for the coefficients of symmetry adapted functions referred to conveniently oriented symmetry axes is given for all rotational point groups. The expression involves the computation of reduced Wigner-matrix elements corresponding to an angle specific to each group and has the computational advantage of leading to Fourier-space TEM (transmission electron microscopy) reconstruction procedures involving only real valued unknowns. Using this expression, a protocol for ab initio view and center assignment and reconstruction so far used for icosahedral particles has been tested with experimental data in other point groups. Copyright © 2013 Elsevier Inc. All rights reserved.

  16. Symmetry-adapted Liouville space. Pt. 7

    International Nuclear Information System (INIS)

    Temme, F.P.

    1990-01-01

    In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over vertical strokekqv>> operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such (k i = 1) nuclear spin clusters. The SU2 X S n group provides the essential mappings and the form of H carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced S n -symmetry. (orig.)

  17. Quantum Space-Time Deformed Symmetries Versus Broken Symmetries

    CERN Document Server

    Amelino-Camelia, G

    2002-01-01

    Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical Lorentz symmetries. I compare two interesting cases: the case in which the classical symmetries are "broken", i.e. at the quantum level some classical symmetries are lost, and the case in which the classical symmetries are "deformed", i.e. the quantum space-time has as many symmetries as its classical counterpart but the nature of these symmetries is affected by the space-time quantization procedure. While some general features, such as the emergence of deformed dispersion relations, characterize both the symmetry-breaking case and the symmetry-deformation case, the two scenarios are also characterized by sharp differences, even concerning the nature of the new effects predicted. I illustrate this point within an illustrative calculation concerning the role of space-time symm...

  18. Evidence for monoclinic distortion in the ground state phase of underdoped La_1_._9_5Sr_0_._0_5CuO_4: A single crystal neutron diffraction study

    International Nuclear Information System (INIS)

    Singh, Anar; Schefer, Jürg; Frontzek, Matthias; Sura, Ravi; Conder, Kazimierz; Sibille, Romain F.; Ceretti, Monica; Paulus, Werner

    2016-01-01

    The existing controversy about the symmetry of the crystal structure of the ground state of the critical doped La_1_._9_5Sr_0_._0_5CuO_4 has been resolved by analyzing the single crystal neutron diffraction data collected between 5 and 730 K. We observed small but significant intensities for “forbidden” reflections given by extinction rules of the orthorhombic Bmab space group at low temperatures. A careful investigation of neutron diffraction data reveals that the crystal structure of La_1_._9_5Sr_0_._0_5CuO_4 at 5 K is monoclinic with B2/m (2/m 1 1) space group. The monoclinic structure emerges from the orthorhombic structure in a continuous way; however, the structure is stable below ∼120 K which agrees with other observed phenomena. Our results on symmetry changes are crucial for the interpretation of physical properties also in other high temperature superconductors with similar structures.

  19. Group quantization on configuration space: Gauge symmetries and linear fields

    International Nuclear Information System (INIS)

    Navarro, M.; Aldaya, V.; Calixto, M.

    1997-01-01

    A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyze, in a systematic manner and with complete generality, the case of linear fields (Abelian current groups). To illustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the Abelian Chern endash Simons models over an arbitrary closed surface in detail. copyright 1997 American Institute of Physics

  20. Static deformation of two welded monoclinic elastic half-spaces due ...

    Indian Academy of Sciences (India)

    M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22

    Static deformation of two monoclinic elastic half-spaces in welded contact due to a long inclined strike-slip fault situated in one of the half-spaces is studied analytically and numerically. Closed- form algebraic expressions for the displacement at any point of the medium are obtained. The variation of the displacement at the ...

  1. The Poincare group as the symmetry group of canonical general relativity

    International Nuclear Information System (INIS)

    Beig, R.; Murchadha, N. o

    1986-01-01

    This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to General Relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincare group acts as a symmetry group on the phase space of G.R. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained. (Author)

  2. Space-Time Crystal and Space-Time Group.

    Science.gov (United States)

    Xu, Shenglong; Wu, Congjun

    2018-03-02

    Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.

  3. A monoclinic polymorph of (1E,5E)-1,5-bis­(2-hy­droxy­benzyl­idene)thio­carbono­hydrazide

    Science.gov (United States)

    Schmitt, Bonell; Gerber, Thomas; Hosten, Eric; Betz, Richard

    2011-01-01

    The title compound, C15H14N4O2S, is a derivative of thio­ureadihydrazide. In contrast to the previously reported polymorph (ortho­rhom­bic, space group Pbca, Z = 8), the current study revealed monoclinic symmetry (space group P21/n, Z = 4). The mol­ecule shows non-crystallographic C 2 as well as approximate C s symmetry. Intra­molecular bifurcated O—H⋯(N,S) hydrogen bonds, are present. In the crystal, inter­molecular N—H⋯S hydrogen bonds and C—H⋯π contacts connect the mol­ecules into undulating chains along the b axis. The shortest centroid–centroid distance between two aromatic systems is 4.5285 (12) Å. PMID:22091213

  4. Quregisters, Symmetry Groups and Clifford Algebras

    International Nuclear Information System (INIS)

    Cervantes, D; Morales-Luna, G

    2016-01-01

    Natural one-to-one and two-to-one homomorphisms from SO(3) into SU(2) are built conventionally, and the collection of qubits, is identified with a subgroup of SU(2). This construction is suitable to be extended to corresponding tensor powers. The notions of qubits, quregisters and qugates are translated into the language of symmetry groups. The corresponding elements to entangled states in the tensor product of Hilbert spaces reflect entanglement properties as well, and in this way a notion of entanglement is realised in the tensor product of symmetry groups. (paper)

  5. Quantum group and quantum symmetry

    International Nuclear Information System (INIS)

    Chang Zhe.

    1994-05-01

    This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schroedinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion. (author). 133 refs, 20 figs

  6. Determination of Stress Coefficient Terms in Cracked Solids for Monoclinic Materials with Plane Symmetry at x3 = 0

    Science.gov (United States)

    Yuan, F. G.

    1998-01-01

    Determination of all the coefficients in the crack tip field expansion for monoclinic materials under two-dimensional deformation is presented in this report. For monoclinic materials with a plane of material symmetry at x(sub 3) = 0, the in-plane deformation is decoupled from the anti-plane deformation. In the case of in-plane deformation, utilizing conservation laws of elasticity and Betti's reciprocal theorem, together with selected auxiliary fields, T-stress and third-order stress coefficients near the crack tip are evaluated first from path-independent line integrals. To determine the T-stress terms using the J-integral and Betti's reciprocal work theorem, auxiliary fields under a concentrated force and moment acting at the crack tip are used respectively. Through the use of Stroh formalism in anisotropic elasticity, analytical expressions for all the coefficients including the stress intensity factors are derived in a compact form that has surprisingly simple structure in terms of the Barnett-Lothe tensors, L. The solution forms for degenerated materials, orthotropic, and isotropic materials are presented.

  7. On the characterization of infinitesimal symmetries of the relativistic phase space

    International Nuclear Information System (INIS)

    Janyška, Josef; Vitolo, Raffaele

    2012-01-01

    The phase space of relativistic particle mechanics is defined as the first jet space of motions regarded as time-like one-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally a generalized contact structure on the odd-dimensional phase space. In the paper, infinitesimal symmetries of the phase structures are characterized. More precisely, it is proved that all phase infinitesimal symmetries are special Hamiltonian lifts of distinguished conserved quantities on the phase space. It is proved that generators of infinitesimal symmetries constitute a Lie algebra with respect to a special bracket. A momentum map for groups of symmetries of the geometric structures is provided. (paper)

  8. Physical symmetry groups and associated bundles in field theory

    International Nuclear Information System (INIS)

    Crumeyrolle, A.

    1986-01-01

    A previous paper, ''Some geometrical consequences of physical symmetries'' describes in some detail invariant submanifolds of the linear representation space C /sup 4m/ for the physical symmetry group : SU(2,2)xSU(m) and its subgroup PxSU(m). In this paper the author intends to give a geometric version using homogeneous spaces and a spinorial approach. Some concrete orbits by means of spinor structures considered in the modern scope and some plausible physical consequences are discussed

  9. Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space

    International Nuclear Information System (INIS)

    Haapasalo, Erkka Theodor; Pellonpaeae, Juha-Pekka

    2011-01-01

    We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference, and time observables.

  10. Possible bicollinear nematic state with monoclinic lattice distortions in iron telluride compounds

    Energy Technology Data Exchange (ETDEWEB)

    Bishop, Christopher B. [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Herbrych, Jacek W. [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Dagotto, Elbio R. [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Moreo, Adriana [Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2017-07-15

    Here, iron telluride (FeTe) is known to display bicollinear magnetic order at low temperatures together with a monoclinic lattice distortion. Because the bicollinear order can involve two different wave vectors (π/2,π/2) and (π/2,–π/2), symmetry considerations allow for the possible stabilization of a nematic state with short-range bicollinear order coupled to monoclinic lattice distortions at a TS higher than the temperature TN where long-range bicollinear order fully develops. As a concrete example, the three-orbital spin-fermion model for iron telluride is studied with an additional coupling ˜λ12 between the monoclinic lattice strain and an orbital-nematic order parameter with B2g symmetry. Monte Carlo simulations show that with increasing ˜λ12 the first-order transition characteristic of FeTe splits and bicollinear nematicity is stabilized in a (narrow) temperature range. In this new regime, the lattice is monoclinically distorted and short-range spin and orbital order breaks rotational invariance. A discussion of possible realizations of this exotic state is provided.

  11. On the Lie symmetry group for classical fields in noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)

    2011-07-01

    Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)

  12. The giant piezoelectric effect: electric field induced monoclinic phase or piezoelectric distortion of the rhombohedral parent?

    CERN Document Server

    Kisi, E H; Forrester, J S; Howard, C J

    2003-01-01

    Lead zinc niobate-lead titanate (PZN-PT) single crystals show very large piezoelectric strains for electric fields applied along the unit cell edges e.g. [001] sub R. It has been widely reported that this effect is caused by an electric field induced phase transition from rhombohedral (R3m) to monoclinic (Cm or Pm) symmetry in an essentially continuous manner. Group theoretical analysis using the computer program ISOTROPY indicates phase transitions between R3m and Cm (or Pm) must be discontinuous under Landau theory. An analysis of the symmetry of a strained unit cell in R3m and a simple expansion of the piezoelectric strain equation indicate that the piezoelectric distortion due to an electric field along a cell edge in rhombohedral perovskite-based ferroelectrics is intrinsically monoclinic (Cm), even for infinitesimal electric fields. PZN-PT crystals have up to nine times the elastic compliance of other piezoelectric perovskites and it might be expected that the piezoelectric strains are also very large. ...

  13. On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation

    International Nuclear Information System (INIS)

    Burdík, C; Reshetnyak, A

    2012-01-01

    We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.

  14. Discrete symmetries and coset space dimensional reduction

    International Nuclear Information System (INIS)

    Kapetanakis, D.; Zoupanos, G.

    1989-01-01

    We consider the discrete symmetries of all the six-dimensional coset spaces and we apply them in gauge theories defined in ten dimensions which are dimensionally reduced over these homogeneous spaces. Particular emphasis is given in the consequences of the discrete symmetries on the particle content as well as on the symmetry breaking a la Hosotani of the resulting four-dimensional theory. (orig.)

  15. Reflection of P and SV waves at the free surface of a monoclinic ...

    Indian Academy of Sciences (India)

    The propagation of plane waves in an anisotropic elastic medium possessing monoclinic symmetry is discussed. The expressions for the phase velocity of qP and qSV waves propagating in the plane of elastic symmetry are obtained in terms of the direction cosines of the propagation vector. It is shown that, in general, ...

  16. Evidence for photo-induced monoclinic metallic VO2 under high pressure

    International Nuclear Information System (INIS)

    Hsieh, Wen-Pin; Mao, Wendy L.; Trigo, Mariano; Reis, David A.; Andrea Artioli, Gianluca; Malavasi, Lorenzo

    2014-01-01

    We combine ultrafast pump-probe spectroscopy with a diamond-anvil cell to decouple the insulator-metal electronic transition from the lattice symmetry changing structural transition in the archetypal strongly correlated material vanadium dioxide. Coherent phonon spectroscopy enables tracking of the photo-excited phonon vibrational frequencies of the low temperature, monoclinic (M 1 )-insulating phase that transforms into the metallic, tetragonal rutile structured phase at high temperature or via non-thermal photo-excitations. We find that in contrast with ambient pressure experiments where strong photo-excitation promptly induces the electronic transition along with changes in the lattice symmetry, at high pressure, the coherent phonons of the monoclinic (M 1 ) phase are still clearly observed upon the photo-driven phase transition to a metallic state. These results demonstrate the possibility of synthesizing and studying transient phases under extreme conditions

  17. Projective unitary-antiunitary representations of the Shubnikov space groups

    International Nuclear Information System (INIS)

    Broek, P.M. van den.

    1979-01-01

    Some mathematical aspects of the symmetry of a physical system in quantum mechanics are examined with special emphasis on the symmetry groups of charged particles in crystalline solids, the Shuknikov space groups. (Auth.)

  18. Evidence for photo-induced monoclinic metallic VO{sub 2} under high pressure

    Energy Technology Data Exchange (ETDEWEB)

    Hsieh, Wen-Pin, E-mail: wphsieh@stanford.edu; Mao, Wendy L. [Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States); Department of Geological and Environmental Sciences, Stanford University, Stanford, California 94305 (United States); Trigo, Mariano [Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States); Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States); Reis, David A. [Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States); Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States); Department of Photon Science and Applied Physics, Stanford University, Stanford, California 94305 (United States); Andrea Artioli, Gianluca; Malavasi, Lorenzo [Dipartimento di Chimica, Sezione di Chimica Fisica, INSTM (UdR Pavia), Università di Pavia, Viale Taramelli 16, 27100 Pavia (Italy)

    2014-01-13

    We combine ultrafast pump-probe spectroscopy with a diamond-anvil cell to decouple the insulator-metal electronic transition from the lattice symmetry changing structural transition in the archetypal strongly correlated material vanadium dioxide. Coherent phonon spectroscopy enables tracking of the photo-excited phonon vibrational frequencies of the low temperature, monoclinic (M{sub 1})-insulating phase that transforms into the metallic, tetragonal rutile structured phase at high temperature or via non-thermal photo-excitations. We find that in contrast with ambient pressure experiments where strong photo-excitation promptly induces the electronic transition along with changes in the lattice symmetry, at high pressure, the coherent phonons of the monoclinic (M{sub 1}) phase are still clearly observed upon the photo-driven phase transition to a metallic state. These results demonstrate the possibility of synthesizing and studying transient phases under extreme conditions.

  19. Group analysis and renormgroup symmetries

    International Nuclear Information System (INIS)

    Kovalev, V.F.; Pustovalov, V.V.; Shirkov, D.V.

    1996-01-01

    An original regular approach to constructing special type symmetries for boundary-value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model. 35 refs

  20. Space-time and Local Gauge Symmetries

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Symmetries of Particle Physics: Space-time and Local Gauge Symmetries. Sourendu Gupta. General Article Volume 6 Issue 2 February 2001 pp 29-38. Fulltext. Click here to view fulltext PDF. Permanent link:

  1. Room Temperature Monoclinic Phase in BaTiO3 Single Crystals

    Science.gov (United States)

    Denev, Sava; Kumar, Amit; Barnes, Andrew; Vlahos, Eftihia; Shepard, Gabriella; Gopalan, Venkatraman

    2010-03-01

    BaTiO3 is a well studied ferroelectric material for the last half century. It is well known to show phase transitions to tetragonal, orthorhombic and rhombohedral phases upon cooling. Yet, some old and some recent studies have argued that all these phases co-exist with a second phase with monoclinic distortion. Using optical second harmonic generation (SHG) at room temperature we directly present evidence for such monoclininc phase co-existing with tetragonal phase at room temperature. We observe domains with the expected tetragonal symmetry exhibiting 90^o and 180^o domain walls. However, at points of higher stress at the tips of the interpenetrating tetragonal domains we observe a well pronounced metastable ``staircase pattern'' with a micron-scale fine structure. Polarization studies show that this phase can be explained only by monoclinic symmetry. This phase is very sensitive to external perturbations such as temperature and fields, hence stabilizing this phase at room temperature could lead to large properties' tunability.

  2. Mixed-symmetry fields in de Sitter space: a group theoretical glance

    Energy Technology Data Exchange (ETDEWEB)

    Basile, Thomas [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS,Fédération de Recherche 2964 Denis Poisson, Université François Rabelais,Parc de Grandmont, 37200 Tours (France); Groupe de Mécanique et Gravitation, Service de Physique Théorique et Mathématique,Université de Mons - UMONS,20 Place du Parc, 7000 Mons, Belgique (Belgium); Bekaert, Xavier [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS,Fédération de Recherche 2964 Denis Poisson, Université François Rabelais,Parc de Grandmont, 37200 Tours (France); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science,Daejeon (Korea, Republic of); Boulanger, Nicolas [Groupe de Mécanique et Gravitation, Service de Physique Théorique et Mathématique,Université de Mons - UMONS,20 Place du Parc, 7000 Mons, Belgique (Belgium)

    2017-05-15

    We derive the characters of all unitary irreducible representations of the (d+1)-dimensional de Sitter spacetime isometry algebra so(1,d+1), and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We identify the equivalent of the scalar singleton for the de Sitter (dS) spacetime.

  3. Internal space-time symmetries of massive and massless particles and their unification

    International Nuclear Information System (INIS)

    Kim, Y.S.

    2001-01-01

    It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to its helicity, the two translational degrees of freedom correspond to its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like symmetry of massive particles. This mechanism is illustrated in terms of a sphere elongating into a cylinder. In this way, the helicity degree of freedom remains invariant under the Lorentz boost, but the transverse rotational degrees of freedom become contracted into the gauge degree of freedom

  4. Symmetry and group theory throughout physics

    Directory of Open Access Journals (Sweden)

    Villain J.

    2012-03-01

    Full Text Available As noticed in 1884 by Pierre Curie [1], physical properties of matter are tightly related to the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and eigenvalues of an operator. Certain properties (optical activity, piezoelectricity are forbidden in molecules or crystals of high symmetry. A few theorems (Noether, Goldstone establish general relations between physical properties and symmetry. Applications of group theory to condensed matter physics, elementary particle physics, quantum mechanics, electromagnetism are reviewed. Group theory is not only a tool, but also a beautiful construction which casts insight into natural phenomena.

  5. Space groups for solid state scientists

    CERN Document Server

    Glazer, Michael; Glazer, Alexander N

    2014-01-01

    This Second Edition provides solid state scientists, who are not necessarily experts in crystallography, with an understandable and comprehensive guide to the new International Tables for Crystallography. The basic ideas of symmetry, lattices, point groups, and space groups are explained in a clear and detailed manner. Notation is introduced in a step-by-step way so that the reader is supplied with the tools necessary to derive and apply space group information. Of particular interest in this second edition are the discussions of space groups application to such timely topics as high-te

  6. The giant piezoelectric effect: electric field induced monoclinic phase or piezoelectric distortion of the rhombohedral parent?

    International Nuclear Information System (INIS)

    Kisi, E H; Piltz, R O; Forrester, J S; Howard, C J

    2003-01-01

    Lead zinc niobate-lead titanate (PZN-PT) single crystals show very large piezoelectric strains for electric fields applied along the unit cell edges e.g. [001] R . It has been widely reported that this effect is caused by an electric field induced phase transition from rhombohedral (R3m) to monoclinic (Cm or Pm) symmetry in an essentially continuous manner. Group theoretical analysis using the computer program ISOTROPY indicates phase transitions between R3m and Cm (or Pm) must be discontinuous under Landau theory. An analysis of the symmetry of a strained unit cell in R3m and a simple expansion of the piezoelectric strain equation indicate that the piezoelectric distortion due to an electric field along a cell edge in rhombohedral perovskite-based ferroelectrics is intrinsically monoclinic (Cm), even for infinitesimal electric fields. PZN-PT crystals have up to nine times the elastic compliance of other piezoelectric perovskites and it might be expected that the piezoelectric strains are also very large. A field induced phase transition is therefore indistinguishable from the piezoelectric distortion and is neither sufficient nor necessary to understand the large piezoelectric response of PZN-PT

  7. Exploiting Stabilizers and Parallelism in State Space Generation with the Symmetry Method

    DEFF Research Database (Denmark)

    Lorentsen, Louise; Kristensen, Lars Michael

    2001-01-01

    The symmetry method is a main reduction paradigm for alleviating the state explosion problem. For large symmetry groups deciding whether two states are symmetric becomes time expensive due to the apparent high time complexity of the orbit problem. The contribution of this paper is to alleviate th...... the negative impact of the orbit problem by the specification of canonical representatives for equivalence classes of states in Coloured Petri Nets, and by giving algorithms exploiting stabilizers and parallelism for computing the condensed state space.......The symmetry method is a main reduction paradigm for alleviating the state explosion problem. For large symmetry groups deciding whether two states are symmetric becomes time expensive due to the apparent high time complexity of the orbit problem. The contribution of this paper is to alleviate...

  8. Symmetries and groups in particle physics

    International Nuclear Information System (INIS)

    Scherer, Stefan

    2016-01-01

    The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to

  9. High-field Transport in Low Symmetry β-Ga2O3 Crystal

    Science.gov (United States)

    Ghosh, Krishnendu; Singisetti, Uttam

    High-field carrier transport plays an important role in many disciplines of electronics. Conventional transport theories work well on high-symmetry materials but lacks insight as the crystal symmetry goes down. Newly emerging materials, many of which possess low symmetry, demand more rigorous treatment of charge transport. We will present a comprehensive study of high-field transport using ab initio electron-phonon interaction (EPI) elements in a full-band Monte Carlo (FBMC) algorithm. We use monoclinic β-Ga2O3 as a benchmark low-symmetry material which is also an emerging wide-bandgap semiconductor. β-Ga2O3 has a C2m space group and a 10 atom primitive cell. In this work the EPIs are calculated under density-functional perturbation theory framework. We will focus on the computational challenges arising from many phonon modes and low crystal symmetry. Significant insights will be presented on the details of energy relaxation by the hot electrons mediated by different phonon modes. We will also show the velocity-field curves of electrons in different crystal directions. The authors acknowledge the support from the National Science Foundation Grant (ECCS 1607833). The authors also acknowledge the computing support provided by the Center for Computational Research at the University at Buffalo.

  10. Anisotropy and phonon modes from analysis of the dielectric function tensor and the inverse dielectric function tensor of monoclinic yttrium orthosilicate

    Science.gov (United States)

    Mock, A.; Korlacki, R.; Knight, S.; Schubert, M.

    2018-04-01

    We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40-1200 cm-1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017), 10.1103/PhysRevB.95.165202], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016), 10.1103/PhysRevLett.117.215502].

  11. Some symmetries in nuclei

    International Nuclear Information System (INIS)

    Henley, E.M.

    1981-09-01

    Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces

  12. Groups and Symmetry

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. Groups and Symmetry: A Guide to Discovering Mathematics. Geetha Venkataraman. Book Review Volume 4 Issue 10 October 1999 pp 91-92. Fulltext. Click here to view fulltext PDF. Permanent link:

  13. Unified Symmetry of Nonholonomic System of Non-Chetaev's Type in Event Space

    International Nuclear Information System (INIS)

    Hou Qibao; Li Yuancheng; Wang Jing; Xia Lili

    2007-01-01

    The unified symmetry of a nonholonomic system of non-Chetaev's type in event space under infinitesimal transformations of group is studied. Firstly, the differential equations of motion of the system are given. Secondly, the definition and the criterion of the unified symmetry for the system are obtained. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev's type. Finally, an example is given to illustrate the application of the result.

  14. Superspace group descriptions of the symmetries of incommensurate urea inclusion compounds

    NARCIS (Netherlands)

    vanSmaalen, S; Harris, KDM

    1996-01-01

    Urea inclusion compounds are a class of incommensurate composite crystals. The urea molecules form a three-dimensionally connected network, with approximate space group symmetry P6(1)22. This network contains tunnels (channels), which accommodate guest molecules. The periodicities of the urea

  15. Causality and symmetry in cosmology and the conformal group

    International Nuclear Information System (INIS)

    Segal, I.E.

    1977-01-01

    A new theoretic postulate in fundamental physics is considered which is called the chronometric principle because it deals primarily with the nature of time, or its dual or conjugate, energy. Conformality is equivalent to causality. Thus, the group of all local causality-preserving transformations in the vicinity of a point of Minkowski space is, as a local Lie group, identical with the conformal group. The same statement made globally on Minkowski space is: The set of all vector fields on Minkowski space which generate smooth local causality-preserving transformations is identical with the set of all conformal vector fields. The main validation for the chronometric principle is in cosmology or ultramacroscopic physics. Therefore this principle is illustrated along the lines of the red shift. This principle in combination with quantum field theory leads to a convergent and causal description of particle production in which nonlinearities are supplanted by more sophisticated and comprehensive actions for the fundamental symmetry groups. 11 references

  16. Early space symmetry restoration and neutrino experiments

    International Nuclear Information System (INIS)

    Volkov, G.G.; Liparteliani, A.G.; Monich, V.A.

    1986-01-01

    The problem of early space symmetry restoration on the left-right symmetry models and the models with the extended (due to mirror quarks and leptons) fermion sector is being discussed. The experiments in which the derivations from the standard model of electroweak interactions should be studied are presented

  17. Non-commutative phase space and its space-time symmetry

    International Nuclear Information System (INIS)

    Li Kang; Dulat Sayipjamal

    2010-01-01

    First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)

  18. Asymptotic symmetries of Rindler space at the horizon and null infinity

    International Nuclear Information System (INIS)

    Chung, Hyeyoun

    2010-01-01

    We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.

  19. Group theory of spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    Ghaboussi, F.

    1987-01-01

    The connection between the minimality of the Higgs field potential and the maximal little groups of its representation obtained by spontaneous symmetry breaking is analyzed. It is shown that for several representations the lowest minimum of the potential is related to the maximal little group of those representations. Furthermore, a practical necessity criterion is given for the representation of the Higgs field needed for spontaneous symmetry breaking

  20. Discrete symmetries for spinor field in de Sitter space

    International Nuclear Information System (INIS)

    Moradi, S.; Rouhani, S.; Takook, M.V.

    2005-01-01

    Discrete symmetries, parity, time reversal, antipodal, and charge conjugation transformations for spinor field in de Sitter space, are presented in the ambient space notation, i.e., in a coordinate independent way. The PT and PCT transformations are also discussed in this notation. The five-current density is studied and their transformation under the discrete symmetries is discussed

  1. QCD-instantons and conformal space-time inversion symmetry

    International Nuclear Information System (INIS)

    Klammer, D.

    2008-04-01

    In this paper, we explore the appealing possibility that the strong suppression of large-size QCD instantons - as evident from lattice data - is due to a surviving conformal space-time inversion symmetry. This symmetry is both suggested from the striking invariance of highquality lattice data for the instanton size distribution under inversion of the instanton size ρ→(left angle ρ right angle 2 )/(ρ) and from the known validity of space-time inversion symmetry in the classical instanton sector. We project the instanton calculus onto the four-dimensional surface of a five-dimensional sphere via conformal stereographic mapping, before investigating conformal inversion. This projection to a compact, curved geometry is both to avoid the occurence of divergences and to introduce the average instanton size left angle ρ right angle from the lattice data as a new length scale. The average instanton size is identified with the radius b of this 5d-sphere and acts as the conformal inversion radius. For b= left angle ρ right angle, our corresponding results are almost perfectly symmetric under space-time inversion and in good qualitative agreement with the lattice data. For (ρ)/(b)→0 we recover the familiar results of instanton perturbation theory in flat 4d-space. Moreover, we illustrate that a (weakly broken) conformal inversion symmetry would have significant consequences for QCD beyond instantons. As a further successful test for inversion symmetry, we present striking implications for another instanton dominated lattice observable, the chirality-flip ratio in the QCD vacuum. (orig.)

  2. Broken symmetry of Lie groups of transformation generating general relativistic theories of gravitation

    International Nuclear Information System (INIS)

    Halpern, L.

    1981-01-01

    Invariant varieties of suitable semisimple groups of transformations can serve as models of the space-time of the universe. The metric is expressible in terms of the basis vectors of the group. The symmetry of the group is broken by introducing a gauge formalism in the space of the basis vectors with the adjoint group as gauge group. The gauge potentials are expressible in terms of the basis vectors for the case of the De Sitter group. The resulting gauge theory is equivalent to De Sitter covariant general relativity. Group covariant generalizations of gravitational theory are discussed. (Auth.)

  3. Electric-field-induced monoclinic phase in (Ba,Sr)TiO3 thin film

    International Nuclear Information System (INIS)

    Anokhin, A. S.; Yuzyuk, Yu. I.; Golovko, Yu. I.; Mukhortov, V. M.; El Marssi, M.

    2011-01-01

    We have studied electric-field-induced symmetry lowering in the tetragonal (001)-oriented heteroepitaxial (Ba 0.8 Sr 0.2 )TiO 3 thin film deposited on (001)MgO substrate. Polarized micro-Raman spectra were recorded from the film area in between two planar electrodes deposited on the film surface. Presence of c domains with polarization normal to the substrate was confirmed from polarized Raman study under zero field, while splitting and hardening of the E(TO) soft mode and polarization changes in the Raman spectra suggest monoclinic symmetry under external electric field.

  4. sl (6,r) as the group of symmetries for non relativistic quantum systems

    African Journals Online (AJOL)

    It is shown that the 13 one parameter generators of the Lie group SL(6, R) are the maximal group of symmetries for nonrelativistic quantum systems. The group action on the set of states S Ĥ (H complex Hilbert space) preserves transition probabilities as well as the dynamics of the system. By considering a prolongation of ...

  5. Exploiting Stabilizers and Parallelism in State Space Generation with the Symmetry Method

    DEFF Research Database (Denmark)

    Lorentsen, Louise; Kristensen, Lars Michael

    2001-01-01

    The symmetry method is a main reduction paradigm for alleviating the state explosion problem. For large symmetry groups deciding whether two states are symmetric becomes time expensive due to the apparent high time complexity of the orbit problem. The contribution of this paper is to alleviate th...... the negative impact of the orbit problem by the specification of canonical representatives for equivalence classes of states in Coloured Petri Nets, and by giving algorithms exploiting stabilizers and parallelism for computing the condensed state space....

  6. Singular solutions of renormalization group equations and the symmetry of the lagrangian

    International Nuclear Information System (INIS)

    Kazakov, D.I.; Shirokov, D.V.

    1975-01-01

    On the basis of solution of the differential renormalization group equations the method is proposed for finding out the Lagrangians possessing some king of internal symmetry. It is shown that in the phase space of the invariant charges the symmetry corresponds to the straight-line singular solution of these equations remaining straight-line when taking into account the higher order corrections. We have studied the model of scalar fields with quartic couplings, as well as the set of models containing scalar, pseudoscalar and spinor fields with Yukawa and quartic interactions. Straight-line singular solutions in the first case correspond to isotopic symmetry only. For the second case they correspond to supersymmetry. No other symmetries have been discovered. For the model containing the gauge fields the solution corresponding to supersymmetry is obtained and it is shown that this is also the only symmetry that can be realized in the given set of fields

  7. Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups

    CERN Document Server

    2017-01-01

    Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...

  8. Discovering Symmetry in Everyday Environments: A Creative Approach to Teaching Symmetry and Point Groups

    Science.gov (United States)

    Fuchigami, Kei; Schrandt, Matthew; Miessler, Gary L.

    2016-01-01

    A hands-on symmetry project is proposed as an innovative way of teaching point groups to undergraduate chemistry students. Traditionally, courses teaching symmetry require students to identify the point group of a given object. This project asks the reverse: students are instructed to identify an object that matches each point group. Doing so…

  9. Spontaneous symmetry breaking in curved space-time

    International Nuclear Information System (INIS)

    Toms, D.J.

    1982-01-01

    An approach dealing with some of the complications which arise when studying spontaneous symmetry breaking beyond the tree-graph level in situations where the effective potential may not be used is discussed. These situations include quantum field theory on general curved backgrounds or in flat space-times with non-trivial topologies. Examples discussed are a twisted scalar field in S 1 xR 3 and instabilities in an expanding universe. From these it is seen that the topology and curvature of a space-time may affect the stability of the vacuum state. There can be critical length scales or times beyond which symmetries may be broken or restored in certain cases. These features are not present in Minkowski space-time and so would not show up in the usual types of early universe calculations. (U.K.)

  10. Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application.

    Science.gov (United States)

    Stróż, Kazimierz

    2011-09-01

    A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic

  11. Hidden Uq (sl(2)) Uq (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

    Science.gov (United States)

    Cremmer, Eugène; Gervais, Jean-Loup; Schnittger, Jens

    1997-02-01

    In a previous paper, the quantum-group-covariant chiral vertex operators in the spin 1/2 representation were shown to act, by braiding with the other covariant primaries, as generators of the well known Uq(sl(2)) quantum group symmetry (for a single screening charge). Here, this structure is transformed to the Bloch wave/Coulomb gas operator basis, thereby establishing for the first time its quantum group symmetry properties. A Uq(sl(2)) otimes Uq(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (Vermamodules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of the operator product. This hidden symmetry possesses a novel Hopf-like structure compatible with these conditions. At roots of unity it gives the right truncation. Its (non-linear) connection with the Uq(sl(2)) previously discussed is disentangled.

  12. Temperature dependent emission characteristics of monoclinic YBO{sub 3}: Eu{sup 3+}/Tb{sup 3+} phosphor

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Suchinder K., E-mail: suchindersharma@gmail.com [AMO-Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad 380009 (India); Malik, M. Manzar [Department of Physics, Maulana Azad National Institute of Technology (MANIT), Bhopal (India)

    2016-05-15

    YBO{sub 3}:Eu{sup 3+}/Tb{sup 3+} phosphor samples synthesized by modified combustion method are studied in the present work using powder X-ray diffraction, UV–visible absorption spectroscopy, X-ray excited luminescence spectroscopy and optical parametric oscillator (OPO) based laser excited emission spectroscopy. The temperature dependence of luminescence emission is also studied. The structural analysis suggests that the samples possess monoclinic structure with C2/c space group. The emission maximum was excitation wavelength dependent and prominent emission was observed at 593 nm (241 nm excitation) and 613 nm (300 nm excitation) for YBO{sub 3}:Eu{sup 3+} samples. The prominent magnetic/ electric (593/613 nm) dipole-moment allowed transitions are attributed to the presence of Eu{sup 3+} at different sites. For YBO{sub 3}:Tb{sup 3+} phosphor, 543 nm emission was prominent and had no impact of the cite symmetry. The increase in PL intensity in Eu{sup 3+} doped samples above 225 K is associated with the carrier mobility. An energy level scheme showing the positions of the 4f and 5d energy levels of all divalent and trivalent lanthanide ions relative to the valence and conduction band of the YBO{sub 3} has been constructed opening the possibility of using YBO{sub 3} for other interesting applications. - Highlights: • Synthesis of YBO{sub 3} by modified combustion method using glycine as fuel. • Crystallization in monoclinic phase (rarely investigated). • Eu and Tb doping and investigation of temperature dependent PL. • VRBE diagram generated in YBO{sub 3} to develop new optical materials.

  13. Symmetry groups of state vectors in canonical quantum gravity

    International Nuclear Information System (INIS)

    Witt, D.M.

    1986-01-01

    In canonical quantum gravity, the diffeomorphisms of an asymptotically flat hypersurface S, not connected to the identity, but trivial at infinity, can act nontrivially on the quantum state space. Because state vectors are invariant under diffeomorphisms that are connected to the identity, the group of inequivalent diffeomorphisms is a symmetry group of states associated with S. This group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on S. It is calculated for all hypersurfaces of the form S = S 3 /G-point, where the removed point is thought of as infinity on S and the symmetry group S is the zeroth homotopy group of the group of diffeomorphisms of S 3 /G fixing a point and frame, denoted π 0 Diff/sub F/(S 3 /G). Before calculating π 0 Diff/sub F/ (S 3 /G), it is necessary to find π 0 of the group of diffeomorphisms. Once π 0 Diff(S 3 /G) is known, π 0 Diff/sub x/ 0 (S 3 /G) is calculated using a fiber bundle involving Diff(S 3 /G), Diff/sub x/ 0 (S 3 /G), and S 3 /G. Finally, a fiber bundle involving Diff/sub F/(S 3 /G), Diff(S 3 /G), and the bundle of frames over S 3 /G is used along with π 0 Diff/sub x/ 0 (S 3 /G) to calculate π 0 Diff/sub F/(S 3 /G)

  14. Fluid relabelling symmetries, Lie point symmetries and the Lagrangian map in magnetohydrodynamics and gas dynamics

    International Nuclear Information System (INIS)

    Webb, G M; Zank, G P

    2007-01-01

    We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics (MHD) and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilei group to Lagrange label space, in which the Eulerian position coordinate x is regarded as a function of the Lagrange fluid labels x 0 and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Eulerian Lie point symmetry of the Galilei group. The allowed transformation of the Lagrangian fluid labels x 0 corresponds to a fluid relabelling symmetry, including the case where there is no change in the fluid labels. We also consider a class of three, well-known, scaling symmetries for a gas with a constant adiabatic index γ. These symmetries map onto a modified form of the fluid relabelling symmetry determining equations, with non-zero source terms. We determine under which conditions these symmetries are variational or divergence symmetries of the action, and determine the corresponding Lagrangian and Eulerian conservation laws by use of Noether's theorem. These conservation laws depend on the initial entropy, density and magnetic field of the fluid. We derive the conservation law corresponding to the projective symmetry in gas dynamics, for the case γ = (n + 2)/n, where n is the number of Cartesian space coordinates, and the corresponding result for two-dimensional (2D) MHD, for the case γ = 2. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated. The Lie algebraic symmetry relations between the fluid relabelling symmetries in Lagrange label space, and their commutators with a linear combination of the three symmetries with a constant adiabatic index are delineated

  15. Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups

    International Nuclear Information System (INIS)

    Podles, P.

    1995-01-01

    We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU(2) and SO(3) groups. (orig.)

  16. Molecular symmetry: Why permutation-inversion (PI) groups don't render the point groups obsolete

    Science.gov (United States)

    Groner, Peter

    2018-01-01

    The analysis of spectra of molecules with internal large-amplitude motions (LAMs) requires molecular symmetry (MS) groups that are larger than and significantly different from the more familiar point groups. MS groups are described often by the permutation-inversion (PI) group method. It is shown that point groups still can and should play a significant role together with the PI groups for a class of molecules with internal rotors. In molecules of this class, several simple internal rotors are attached to a rigid molecular frame. The PI groups for this class are semidirect products like H ^ F, where the invariant subgroup H is a direct product of cyclic groups and F is a point group. This result is used to derive meaningful labels for MS groups, and to derive correlation tables between MS groups and point groups. MS groups of this class have many parallels to space groups of crystalline solids.

  17. Path integration on space times with symmetry

    International Nuclear Information System (INIS)

    Low, S.G.

    1985-01-01

    Path integration on space times with symmetry is investigated using a definition of path integration of Gaussian integrators. Gaussian integrators, systematically developed using the theory of projective distributions, may be defined in terms of a Jacobi operator Green function. This definition of the path integral yields a semiclassical expansion of the propagator which is valid on caustics. The semiclassical approximation to the free particle propagator on symmetric and reductive homogeneous spaces is computed in terms of the complete solution of the Jacobi equation. The results are used to test the validity of using the Schwinger-DeWitt transform to compute an approximation to the coincidence limit of a field theory Green function from a WKB propagator. The method is found not to be valid except for certain special cases. These cases include manifolds constructed from the direct product of flat space and group manifolds, on which the free particle WKB approximation is exact and two sphere. The multiple geodesic contribution to 2 > on Schwarzschild in the neighborhood of rho = 3M is computed using the transform

  18. Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space

    International Nuclear Information System (INIS)

    Fang Jianhui; Ding Ning; Wang Peng

    2006-01-01

    In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.

  19. Simple derivation of magnetic space groups

    International Nuclear Information System (INIS)

    Bertaut, E.F.; CEA Centre d'Etudes Nucleaires de Grenoble, 38

    1975-01-01

    The magnetic translation lattices can be described by invariant wave vectors k. Advantages of the wave vector notation over the notations used by Belov et al. and Opechowski et al. are pointed out. In a one-dimensional real representation a space group element (α/tau(1)) has either the character +1 (symmetry element) or -1 (antisymmetry element). Thus the square of any space group operation must have the character +1 in a one-dimensional real representation. This simple ''square criterion'' is used to limit the admissible k-vectors and to derive the family of magnetic space groups, i.e. the set of all possible magnetic space groups, belonging to the same crystallographic space group. In the discussion some useful side results are obtained. Not only the real one-dimensional representations of point groups are connected to real one-dimensional representations of space groups, but a direct connection is shown to exist between one-dimensional complex representations of the point groups 3, 4 and 6 and one-dimensional real representations, belonging to P[001/2]=Psub(2c)(Psub(c))-lattices with screw axes 3 1 , 3 2 , 4 2 , 6 2 and 6 4 . Rules are derived for finding the Belov symbol when the Opechowski-Guccione symbol of the magnetic space group is known and this opportunity is used for correcting errors in the Opechowski-Guccione tables [fr

  20. Symmetry analysis in parametrisation of complex systems

    International Nuclear Information System (INIS)

    Sikora, W; Malinowski, J

    2010-01-01

    The symmetry analysis method based on the theory of group representations is used for description of complex systems and their behavior in this work. The first trial of using the symmetry analysis in modeling of behavior of complex social system is presented. The evacuation of large building scenarios are discussed as transition from chaotic to ordered states, described as movements of individuals according to fields of displacements, calculated correspondingly to given scenario. The symmetry of the evacuation space is taken into account in calculation of displacements field - the displacements related to every point of this space are presented in the coordinate frame in the best way adapted to given symmetry space group, which is the set of basic vectors of irreducible representation of given symmetry group. The results got with using the symmetry consideration are compared with corresponding results calculated under assumption of shortest way to exits (Voronoi assumption).

  1. Symmetry analysis in parametrisation of complex systems

    Energy Technology Data Exchange (ETDEWEB)

    Sikora, W; Malinowski, J, E-mail: sikora@novell.ftj.agh.edu.p [Faculty of Physics and Applied Computer Science, AGH - University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow (Poland)

    2010-03-01

    The symmetry analysis method based on the theory of group representations is used for description of complex systems and their behavior in this work. The first trial of using the symmetry analysis in modeling of behavior of complex social system is presented. The evacuation of large building scenarios are discussed as transition from chaotic to ordered states, described as movements of individuals according to fields of displacements, calculated correspondingly to given scenario. The symmetry of the evacuation space is taken into account in calculation of displacements field - the displacements related to every point of this space are presented in the coordinate frame in the best way adapted to given symmetry space group, which is the set of basic vectors of irreducible representation of given symmetry group. The results got with using the symmetry consideration are compared with corresponding results calculated under assumption of shortest way to exits (Voronoi assumption).

  2. de Sitter group as a symmetry for optical decoherence

    International Nuclear Information System (INIS)

    Baskal, S; Kim, Y S

    2006-01-01

    Stokes parameters form a Minkowskian 4-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincare sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence process through the decaying off-diagonal elements of the density matrix, which yields to an increase in the value of the determinant. It is noted that the O(3, 2) de Sitter group contains two Lorentz subgroups. The change in the determinant in one Lorentz group can be compensated by the other. It is thus possible to describe the decoherence process as a symmetry transformation in the O(3, 2) space. It is shown also that these two coupled Lorentz groups can serve as a concrete example of Feynman's rest of the universe

  3. Arithmetic crystal classes of magnetic symmetries

    International Nuclear Information System (INIS)

    Angelova, M.N.; Boyle, L.L.

    1993-01-01

    The symmetries and properties of a broad class of magnetic crystals are described by magnetic space groups which contain both (unitary) spatial symmetry operations and their combinations with the (anti-unitary operation of) time inversion, 0. The spatial symmetry operations form a halving, non-magnetic, space group H of the magnetic group M such that M=H+aH. As an abstract group the magnetic group M is isomorphic to a non-magnetic group G. The anti-unitary operator a is simply the time inversion 0 when M is a grey group but a product of time inversion with some spatial operation belonging to the coset G-H when M is a black-and-white group. (Author)

  4. Determining Symmetry Properties of Gravitational Fields of Terrestrial Group Planets

    Directory of Open Access Journals (Sweden)

    R.A. Kascheev

    2016-09-01

    Full Text Available Numerous models of gravity fields of the Solar system bodies have been constructed recently owing to successful space missions. These models are sets of harmonic coefficients of gravity potential expansion in series of spherical functions, which is Laplace series. The sets of coefficients are different in quantity of numerical parameters, sources and composition of the initial observational data, methods to obtain and process them, and, consequently, in a variety of properties and accuracy characteristics. For this reason, the task of comparison of different models of celestial bodies considered in the paper is of interest and relevant. The main purpose of this study is comparison of the models of gravitational potential of the Earth, Moon, Mars, and Venus with the quantitative criteria of different types of symmetries developed by us. It is assumed that some particular symmetry of the density distribution function of the planetary body causes similar symmetry of its gravitational potential. The symmetry of gravitational potential, in its turn, imposes additional conditions (restrictions, which must be satisfied by the harmonic coefficients. The paper deals with seven main types of symmetries: central, axial, two symmetries specular relative to the equatorial planes and prime meridian, as well as three rotational symmetries (at π angle around the coordinate system axes. According to the results of calculations carried out for the Earth, Moon, Mars, and Venus, the values of the criteria vary considerably for different types of symmetries and for different planets. It means that the specific value of each criterion corresponding to a particular celestial body is indicative of the properties and internal structure characteristics of the latter and, therefore, it can be used as a tool for comparative planetology. On the basis of the performed calculations, it is possible to distinguish two groups of celestial bodies having similar properties of

  5. Determination of Patterson group symmetry from sparse multi-crystal data sets in the presence of an indexing ambiguity.

    Science.gov (United States)

    Gildea, Richard J; Winter, Graeme

    2018-05-01

    Combining X-ray diffraction data from multiple samples requires determination of the symmetry and resolution of any indexing ambiguity. For the partial data sets typical of in situ room-temperature experiments, determination of the correct symmetry is often not straightforward. The potential for indexing ambiguity in polar space groups is also an issue, although methods to resolve this are available if the true symmetry is known. Here, a method is presented to simultaneously resolve the determination of the Patterson symmetry and the indexing ambiguity for partial data sets. open access.

  6. Symmetry and fermion degeneracy on a lattice

    International Nuclear Information System (INIS)

    Raszillier, H.

    1982-03-01

    In this paper we consider the general form of finite difference approximation to the Dirac (Weyl) Hamiltonian on a lattice and investigate systematically the dependence on symmetry of the number of particles described by it. Our result is, that to a symmetry - expressed by a crystallographic space group - there corresponds a minimal number of particles, which are associated to prescribed points of momentum space (the unit cell of the reciprocal lattice). For convenience of the reader we show, using the existing detailed descriptions of space groups, how these results look for all the relevant (symmorphic) symmetry groups. Only for lattice Hamiltonians with a momentum dependent mass term can this degeneracy be reduced and even eliminated without reducing the symmetry. (orig./HSI)

  7. Temperature renormalization group approach to spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    Manesis, E.; Sakakibara, S.

    1985-01-01

    We apply renormalization group equations that describe the finite-temperature behavior of Green's functions to investigate thermal properties of spontaneous symmetry breaking. Specifically, in the O(N).O(N) symmetric model we study the change of symmetry breaking patterns with temperature, and show that there always exists the unbroken symmetry phase at high temperature, modifying the naive result of leading order in finite-temperature perturbation theory. (orig.)

  8. Rietveld refinement of magnetic structures from pulsed-neutron-source powder-diffraction data

    International Nuclear Information System (INIS)

    Robinson, R.A.; Lawson, A.C.; Larson, A.C.; Von Dreele, R.B.; Goldstone, J.A.

    1994-01-01

    The General Structure Analysis System, GSAS, has recently been modified to include magnetic neutron- scattering cross-sections. Low-temperature diffraction data have been taken on the hexagonal noncollinear antiferromagnet UPdSn on both the HIPD and the NPD powder diffractometers ail LANSCE. The low-resolution data reveal that the magnetic structure has orthorhombic symmetry (magnetic space group P c m'c2 1 ) between 25K and 40K, and monoclinic symmetry (magnetic space group PC 1121 ) below 25K. The high-resolution data reveal that there are structural distortions with corresponding symmetry changes in each of these phases, to give chemical space groups Cmc2 1 and P2 1 , respectively, while the paramagnetic phase above 40K has space group P6 3 mc. Using GSAS, we have refined data sets from both diffractometers simultaneously, including both magnetic and structural cross-sections. Magnetoelastic coefficients for the distortions have been extracted and we have determined the sign of the coupling between the structural monoclinicity and the magnetic monoclinicity. The magnetic results from Rietveld refinement are in good agreement with model fitting to the integrated intensities of seven independent magnetic reflections and these, in turn, agree with measurements made on the same sample using the constant-wavelength reactor technique. Our results therefore validate, to some level, both the technique of using spallation sources for complicated magnetic structures and the specifics of the GSAS Rietveld code

  9. Spinorial charges and their role in the fusion of internal and space-time symmetries

    International Nuclear Information System (INIS)

    Daniel, M.; Ktorides, C.N.

    1976-01-01

    The advent of supersymmetry immediately led to speculations that a non-trivial mixing of internal and space-time symmetries could be achieved within its framework. In fact, the well-known no-go theorems do not apply to the supersymmetry algebra due to the presence, in the latter, of (anticommuting) spinorial charges. However, not until the recent work of Haag, Lopuszanski and Sohnius did a clearcut picture emerge as to how the aforementioned nontrivial mixing can take place. Most notably, the presence of the conformal algebra within the supersymmetry algebra turns out to be vital. The findings of Haag et al. are solidified through an explicit construction which uses as underlying space the pseudo-Euclidean space E(4, 2), i.e. the space for which the conformal group is the group of rotations, and which employs as main tools the spinors associated with the space E(4, 2). The algebro-geometric approach of Cartan is followed in order to understand both the introduction and the properties of these spinors. In this manner, many insights are gained regarding the mathematical foundations of supersymmetry. Thus, the emergence of the anticommutator, rather than the commutator, among spinor charges is fully understood as a natural algebraic consequence and not as an a priori given fact. In addition, it is clearly seen how an (internal) unitary symmetry group can make its appearance within the supersymmetry scheme and verify, via this explicit construction, the results of Haag et al. (Auth.)

  10. Synthesis, Structure and Properties of Various Molecules Based on the 4,8,12-trioxa-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrene System With an Evaluation of the Effect Differing Molecular Substitution Patterns Has on the Space Group Symmetry

    DEFF Research Database (Denmark)

    Faldt, André; Krebs, Frederik C; Thorup, Niels

    1997-01-01

    of opposite chirality are present within the unit cell, Finally compound 13 crystallises in a centrosymmetric space group. The room temperature pyroelectric coefficient of 3 has been determined, The spatial extent of the trioxatriangulene ground system has been perturbed by chemical substitution......4,8,12-Trioxa-4,8,12,12c-tetrahydrodibenzo [cd,mn]pyrene (3),2,6,10-tri-tert-butyl-4,8,12 -trioxa-4,8,12,12c-tetrahydrodibenzo [cd,mn]pyrene (11) and 2,6,10-tri-tert-butyl-4,8,12-trioxa-12c -methyl-4,8,12,12c -tetrahydrodibenzo[cd,mn]pyrene (12)have been synthesised and their crystal structures...... and the effect: of the substitutions upon the space group symmetry of the chemical derivative has been uncovered by X-ray structural resolution, The non-centrosymmetric point group symmetry of the molecules is reflected in a non-centrosymmetric space group symmetry whenever the spatial perturbations do...

  11. Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model

    International Nuclear Information System (INIS)

    Ivanov, Igor P.; Vdovin, E.

    2013-01-01

    Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the Z 4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM. (orig.)

  12. The 27 Possible Intrinsic Symmetry Groups of Two-Component Links

    Directory of Open Access Journals (Sweden)

    Jason Parsley

    2012-02-01

    Full Text Available We consider the “intrinsic” symmetry group of a two-component link L, defined to be the image ∑(L of the natural homomorphism from the standard symmetry group MCG(S3, L to the product MCG(S3 × MCG(L. This group, first defined by Whitten in 1969, records directly whether L is isotopic to a link L′ obtained from L by permuting components or reversing orientations; it is a subgroup of Γ2, the group of all such operations. For two-component links, we catalog the 27 possible intrinsic symmetry groups, which represent the subgroups of Γ2 up to conjugacy. We are able to provide prime, nonsplit examples for 21 of these groups; some are classically known, some are new. We catalog the frequency at which each group appears among all 77,036 of the hyperbolic two-component links of 14 or fewer crossings in Thistlethwaite’s table. We also provide some new information about symmetry groups of the 293 non-hyperbolic two-component links of 14 or fewer crossings in the table.

  13. The Symmetry Group of the Permutahedron

    Science.gov (United States)

    Crisman, Karl-Dieter

    2011-01-01

    Although it can be visualized fairly easily and its symmetry group is easy to calculate, the permutahedron is a somewhat neglected combinatorial object. We propose it as a useful case study in abstract algebra. It supplies concrete examples of group actions, the difference between right and left actions, and how geometry and algebra can work…

  14. X-Ray Diffraction and μ-Raman Investigation of the Monoclinic-Orthorhombic Phase Transition in Th1-xUx(C2O4)2. 2H2O Solid Solutions

    International Nuclear Information System (INIS)

    Clavier, N.; Dacheux, N.; Clavier, N.; Hingant, N.; Dacheux, N.; Barre, N.; Rivenet, M.; Obbade, S.; Abraham, F.

    2010-01-01

    A complete Th 1-x U x (C 2 O 4 ) 2 . 2H 2 O solid solution was prepared by mild hydrothermal synthesis from a mixture of hydrochloric solutions containing cations and oxalic acid. The crystal structure has been solved from twinned single crystals for x=0, 0. 5, and 1 with monoclinic symmetry, space group C2/c, leading to unit cell parameters of a ≅ to 10. 5 Angstroms, b ≅ 8. 5 Angstrom, and c ≅ 9. 6 Angstrom. The crystal structure consists of a two-dimensional arrangement of actinide centers connected through bis-bidentate oxalate ions forming squares. The actinide metal is coordinated by eight oxygen atoms from four oxalate entities and two water oxygen atoms forming a bi-capped square anti-prism. The connection between the layers is assumed by hydrogen bonds between the water molecules and the oxygen of oxalate of an adjacent layer. Under these conditions, the unit cell contains two independent oxalate ions. From high-temperature μ-Raman and X-ray diffraction studies, the compounds were found to undergo a transition to an orthorhombic form (space group Ccca). The major differences in the structural arrangement concern the symmetry of uranium, which decreases from C2 to D2, leading to a unique oxalate group. Consequently, the ν s (C-O) double band observed in the Raman spectra recorded at room temperature turned into a singlet. This transformation was then used to make the phase transition temperature more precise as a function of the uranium content of the sample. (authors)

  15. Space-group approach to two-electron states in unconventional superconductors

    International Nuclear Information System (INIS)

    Yarzhemsky, V. G.

    2008-01-01

    The direct application of the space-group representation theory, makes possible to obtain limitations for the symmetry of SOP on lines and planes of symmetry in one-electron Brillouin zone. In the case of highly symmetric UPt 3 only theoretical nodal structure of IR E 2u is in agreement with all the experimental results. On the other hand, in the case of high-T c superconductors the two electron description of Cooper pairs in D 2h symmetry is not sufficient to describe experimental nodal structure. It was shown that in this case, the nodal structure is the result of underlying interactions between two-electron states and hidden symmetry D-4 h . (author)

  16. Fergusonite-type CeNbO{sub 4+δ}: Single crystal growth, symmetry revision and conductivity

    Energy Technology Data Exchange (ETDEWEB)

    Bayliss, Ryan D. [Department of Materials, Imperial College London, Prince Consort Road, London, SW7 2BP (United Kingdom); Pramana, Stevin S.; An, Tao; Wei, Fengxia; Kloc, Christian L. [School of Materials Science and Engineering, 50 Nanyang Avenue, Nanyang Technological University, 639798 (Singapore); White, Andrew J.P. [Chemical Crystallography Laboratory, Department of Chemistry, Imperial College London, Exhibition Road, London, SW7 2AZ (United Kingdom); Skinner, Stephen J. [Department of Materials, Imperial College London, Prince Consort Road, London, SW7 2BP (United Kingdom); White, Timothy J. [School of Materials Science and Engineering, 50 Nanyang Avenue, Nanyang Technological University, 639798 (Singapore); Baikie, Tom, E-mail: tbaikie@ntu.edu.sg [School of Materials Science and Engineering, 50 Nanyang Avenue, Nanyang Technological University, 639798 (Singapore)

    2013-08-15

    Large fergusonite-type (ABO{sub 4}, A=Ce, B=Nb) oxide crystals, a prototype electrolyte composition for solid oxide fuel cells (SOFC), were prepared for the first time in a floating zone mirror furnace under air or argon atmospheres. While CeNbO{sub 4} grown in air contained CeNbO{sub 4.08} as a minor impurity that compromised structural analysis, the argon atmosphere yielded a single phase crystal of monoclinic CeNbO{sub 4}, as confirmed by selected area electron diffraction, powder and single crystal X-ray diffraction. The structure was determined in the standard space group setting C12/c1 (No. 15), rather than the commonly adopted I12/a1. AC impedance spectroscopy conducted under argon found that stoichiometric CeNbO{sub 4} single crystals showed lower conductivity compared to CeNbO{sub 4+δ} confirming interstitial oxygen can penetrate through fergusonite and is responsible for the higher conductivity associated with these oxides. - Graphical abstract: Large fergusonite-type CeNbO{sub 4} crystals were prepared for the first time in a floating zone mirror furnace. Crystal growth in an argon atmosphere yielded a single phase monoclinic CeNbO4, as confirmed by selected area electron diffraction, powder and single crystal X-ray diffraction. The structure was determined in the standard space group setting C12/c1 (No. 15), rather than the commonly adopted I12/a1. AC impedance spectroscopy found CeNbO{sub 4} single crystals showed lower conductivity compared to CeNbO{sub 4+δ} confirming interstitial oxygen can penetrate through fergusonite and is responsible for the higher conductivity associated with these oxides. Highlights: • Preparation of single crystals of CeNbO{sub 4} using a floating zone mirror furnace. • Correction to the crystal symmetry of the monoclinic form of CeNbO{sub 4}. • Report the conductivity of a single crystal of CeNbO{sub 4}.

  17. On spinless null propagation in five-dimensional space-times with approximate space-like Killing symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Breban, Romulus [Institut Pasteur, Paris Cedex 15 (France)

    2016-09-15

    Five-dimensional (5D) space-time symmetry greatly facilitates how a 4D observer perceives the propagation of a single spinless particle in a 5D space-time. In particular, if the 5D geometry is independent of the fifth coordinate then the 5D physics may be interpreted as 4D quantum mechanics. In this work we address the case where the symmetry is approximate, focusing on the case where the 5D geometry depends weakly on the fifth coordinate. We show that concepts developed for the case of exact symmetry approximately hold when other concepts such as decaying quantum states, resonant quantum scattering, and Stokes drag are adopted, as well. We briefly comment on the optical model of the nuclear interactions and Millikan's oil drop experiment. (orig.)

  18. Computing the Symmetry Groups of the Platonic Solids With the ...

    Indian Academy of Sciences (India)

    In this article we will determine the symmetry groups of the platonic solids by a combination of some elementary group theory and use of the computer algebra package. Maple. The five platonic solids are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosa- hedron. By determining a symmetry group, ...

  19. Groups and symmetry

    CERN Document Server

    Farmer, David W

    1995-01-01

    In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequ

  20. X-Ray diffraction and mu-Raman investigation of the monoclinic-orthorhombic phase transition in Th(1-x)U(x)(C(2)O(4))(2).2H(2)O solid solutions.

    Science.gov (United States)

    Clavier, Nicolas; Hingant, Nina; Rivenet, Murielle; Obbade, Saïd; Dacheux, Nicolas; Barré, Nicole; Abraham, Francis

    2010-02-15

    A complete Th(1-x)U(x)(C(2)O(4))(2).2H(2)O solid solution was prepared by mild hydrothermal synthesis from a mixture of hydrochloric solutions containing cations and oxalic acid. The crystal structure has been solved from twinned single crystals for x = 0, 0.5, and 1 with monoclinic symmetry, space group C2/c, leading to unit cell parameters of a approximately 10.5 A, b approximately 8.5 A, and c approximately 9.6 A. The crystal structure consists of a two-dimensional arrangement of actinide centers connected through bis-bidentate oxalate ions forming squares. The actinide metal is coordinated by eight oxygen atoms from four oxalate entities and two water oxygen atoms forming a bicapped square antiprism. The connection between the layers is assumed by hydrogen bonds between the water molecules and the oxygen of oxalate of an adjacent layer. Under these conditions, the unit cell contains two independent oxalate ions. From high-temperature mu-Raman and X-ray diffraction studies, the compounds were found to undergo a transition to an orthorhombic form (space group Ccca). The major differences in the structural arrangement concern the symmetry of uranium, which decreases from C2 to D2, leading to a unique oxalate group. Consequently, the nu(s)(C-O) double band observed in the Raman spectra recorded at room temperature turned into a singlet. This transformation was then used to make the phase transition temperature more precise as a function of the uranium content of the sample.

  1. Selenomethionine substitution of orotidine-5-monophosphate decarboxylase causes a change in crystal contacts and space group

    DEFF Research Database (Denmark)

    Poulsen, Jens-Christian Navarro; Harris, Pernille; Jensen, Kaj Frank

    2001-01-01

    with the inhibitor 1-(5'-phospho- -D-ribofuranosyl)barbituric acid crystallizes under similar conditions as the native enzyme. In contrast to the native enzyme, where the crystals belong to the orthorhombic space group P212121, the SeMet-substituted enzyme crystallizes in the monoclinic space group P21......-wavelength anomalous dispersion technique, both native and SeMet-substituted proteins have been produced and purified. During the production of SeMet ODCase, it was observed that SeMet was the only amino acid that it was necessary to add to the defined medium during expression. SeMet-substituted ODCase in complex...

  2. Can the family group be a global symmetry

    International Nuclear Information System (INIS)

    Reiss, D.B.

    1982-01-01

    We consider the possibility that the family group may be a spontaneously broken continuous global symmetry. In the context of grand unification, the couplings of the associated Goldstone bosons to fermions can be sufficiently suppressed so as to satisfy the phenomenological bounds. For a maximal family symmetry this requires a large number of Higgs fields. (orig.)

  3. Extremal rotating black holes in the near-horizon limit: Phase space and symmetry algebra

    Directory of Open Access Journals (Sweden)

    G. Compère

    2015-10-01

    Full Text Available We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra. We focus on vacuum solutions to d dimensional Einstein gravity. Each element in the phase space is a geometry with SL(2,R×U(1d−3 isometries which has vanishing SL(2,R and constant U(1 charges. We construct an on-shell vanishing symplectic structure, which leads to an infinite set of symplectic symmetries. In four spacetime dimensions, the phase space is unique and the symmetry algebra consists of the familiar Virasoro algebra, while in d>4 dimensions the symmetry algebra, the NHEG algebra, contains infinitely many Virasoro subalgebras. The nontrivial central term of the algebra is proportional to the black hole entropy. The conserved charges are given by the Fourier decomposition of a Liouville-type stress-tensor which depends upon a single periodic function of d−3 angular variables associated with the U(1 isometries. This phase space and in particular its symmetries can serve as a basis for a semiclassical description of extremal rotating black hole microstates.

  4. High-symmetry organic scintillator systems

    Science.gov (United States)

    Feng, Patrick L.

    2017-07-18

    An ionizing radiation detector or scintillator system includes a scintillating material comprising an organic crystalline compound selected to generate photons in response to the passage of ionizing radiation. The organic compound has a crystalline symmetry of higher order than monoclinic, for example an orthorhombic, trigonal, tetragonal, hexagonal, or cubic symmetry. A photodetector is optically coupled to the scintillating material, and configured to generate electronic signals having pulse shapes based on the photons generated in the scintillating material. A discriminator is coupled to the photon detector, and configured to discriminate between neutrons and gamma rays in the ionizing radiation based on the pulse shapes of the output signals.

  5. High-symmetry organic scintillator systems

    Energy Technology Data Exchange (ETDEWEB)

    Feng, Patrick L.

    2018-03-13

    An ionizing radiation detector or scintillator system includes a scintillating material comprising an organic crystalline compound selected to generate photons in response to the passage of ionizing radiation. The organic compound has a crystalline symmetry of higher order than monoclinic, for example an orthorhombic, trigonal, tetragonal, hexagonal, or cubic symmetry. A photodetector is optically coupled to the scintillating material, and configured to generate electronic signals having pulse shapes based on the photons generated in the scintillating material. A discriminator is coupled to the photon detector, and configured to discriminate between neutrons and gamma rays in the ionizing radiation based on the pulse shapes of the output signals.

  6. High-symmetry organic scintillator systems

    Science.gov (United States)

    Feng, Patrick L.

    2018-02-06

    An ionizing radiation detector or scintillator system includes a scintillating material comprising an organic crystalline compound selected to generate photons in response to the passage of ionizing radiation. The organic compound has a crystalline symmetry of higher order than monoclinic, for example an orthorhombic, trigonal, tetragonal, hexagonal, or cubic symmetry. A photodetector is optically coupled to the scintillating material, and configured to generate electronic signals having pulse shapes based on the photons generated in the scintillating material. A discriminator is coupled to the photon detector, and configured to discriminate between neutrons and gamma rays in the ionizing radiation based on the pulse shapes of the output signals.

  7. Renormalisation group improved leptogenesis in family symmetry models

    International Nuclear Information System (INIS)

    Cooper, Iain K.; King, Stephen F.; Luhn, Christoph

    2012-01-01

    We study renormalisation group (RG) corrections relevant for leptogenesis in the case of family symmetry models such as the Altarelli-Feruglio A 4 model of tri-bimaximal lepton mixing or its extension to tri-maximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of right-handed neutrino masses. More generally, the results of this paper show that RG corrections to leptogenesis cannot be ignored for any family symmetry model involving sizeable neutrino and τ Yukawa couplings.

  8. The information metric on the moduli space of instantons with global symmetries

    Directory of Open Access Journals (Sweden)

    Emanuel Malek

    2016-02-01

    Full Text Available In this note we revisit Hitchin's prescription [1] of the Fisher metric as a natural measure on the moduli space of instantons that encodes the space–time symmetries of a classical field theory. Motivated by the idea of the moduli space of supersymmetric instantons as an emergent space in the sense of the gauge/gravity duality, we extend the prescription to encode also global symmetries of the underlying theory. We exemplify our construction with the instanton solution of the CPN sigma model on R2.

  9. Discrete symmetries in periodic-orbit theory

    International Nuclear Information System (INIS)

    Robbins, J.M.

    1989-01-01

    The application of periodic-orbit theory to systems which possess a discrete symmetry is considered. A semiclassical expression for the symmetry-projected Green's function is obtained; it involves a sum over classical periodic orbits on a symmetry-reduced phase space, weighted by characters of the symmetry group. These periodic orbits correspond to trajectories on the full phase space which are not necessarily periodic, but whose end points are related by symmetry. If the symmetry-projected Green's functions are summed, the contributions of the unperiodic orbits cancel, and one recovers the usual periodic-orbit sum for the full Green's function. Several examples are considered, including the stadium billiard, a particle in a periodic potential, the Sinai billiard, the quartic oscillator, and the rotational spectrum of SF 6

  10. Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

    Science.gov (United States)

    Moretti, Valter; Oppio, Marco

    As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the

  11. Lie symmetries and differential galois groups of linear equations

    NARCIS (Netherlands)

    Oudshoorn, W.R.; Put, M. van der

    2002-01-01

    For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In

  12. Stringy origin of non-Abelian discrete flavor symmetries

    International Nuclear Information System (INIS)

    Kobayashi, Tatsuo; Nilles, Hans Peter; Ploeger, Felix; Raby, Stuart; Ratz, Michael

    2007-01-01

    We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D 4 and Δ(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Abelian flavor symmetries

  13. Universe symmetries

    International Nuclear Information System (INIS)

    Souriau, J.M.

    1984-01-01

    The sky uniformity can be noticed in studying the repartition of objects far enough. The sky isotropy description uses space rotations. The group theory elements will allow to give a meaning at the same time precise and general to the word a ''symmetry''. Universe models are reviewed, which must have both of the following qualities: - conformity with the physic known laws; - rigorous symmetry following one of the permitted groups. Each of the models foresees that universe evolution obeys an evolution equation. Expansion and big-bang theory are recalled. Is universe an open or closed space. Universe is also electrically neutral. That leads to a work hypothesis: the existing matter is not given data of universe but it appeared by evolution from nothing. Problem of matter and antimatter is then raised up together with its place in universe [fr

  14. Symmetries of Ginsparg-Wilson chiral fermions

    International Nuclear Information System (INIS)

    Mandula, Jeffrey E.

    2009-01-01

    The group structure of the variant chiral symmetry discovered by Luescher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter invariant subgroup, and the factor group, whose elements are its cosets, is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, noncommuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example, free overlap fermions, these noncanonical elements of lattice chiral symmetry are related to complex energy singularities that violate reflection positivity and impede continuation to Minkowski space.

  15. Derivation of space groups in mm2, 222 and mmm crystal classes

    International Nuclear Information System (INIS)

    Nigam, G.D.

    1987-08-01

    An algebraic approach is developed to derive space groups using 4x4 Seitz matrices for the crystal classes mm2, 222 and mmm in the orthorhombic system. The advantage of the present method is that it is relatively simple and can be adapted to introduce space groups to beginners. One of the advantages of the present method is that it admits a geometrical visualization of the symmetry elements of space group. The method can easily be extended to other crystal classes in a straightforward way. 16 refs, 1 fig., 2 tabs

  16. Self-consistent Bayesian analysis of space-time symmetry studies

    International Nuclear Information System (INIS)

    Davis, E.D.

    1996-01-01

    We introduce a Bayesian method for the analysis of epithermal neutron transmission data on space-time symmetries in which unique assignment of the prior is achieved by maximisation of the cross entropy and the imposition of a self-consistency criterion. Unlike the maximum likelihood method used in previous analyses of parity-violation data, our method is freed of an ad hoc cutoff parameter. Monte Carlo studies indicate that our self-consistent Bayesian analysis is superior to the maximum likelihood method when applied to the small data samples typical of symmetry studies. (orig.)

  17. Acceleration-enlarged symmetries in nonrelativistic space-time with a cosmological constant TH1"-->

    Science.gov (United States)

    Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J.

    2008-05-01

    By considering the nonrelativistic limit of de Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries that depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new noncommutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one, which possesses acceleration-enlarged Galilean symmetries.

  18. Deformed conformal and super-Poincare symmetries in the non- (anti-) commutative spaces

    International Nuclear Information System (INIS)

    Banerjee, R.; Lee, C.; Siwach, S.

    2006-01-01

    Generators of the super-Poincare algebra in the non- (anti-) commutative superspace are represented using appropriate higher derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the conformal and superconformal symmetry generators in the deformed spaces. This construction is obtained by generalizing the recent work of Wess et al. on the Poincare generators in the θ-deformed Minkowski space, or by using the substitution rules we derived on the basis of the phase-space structures of non- (anti-) commutative-space variables. Even with the non-zero deformation parameters the algebras remain unchanged although the comultiplication rules are deformed. The transformation of the fields under deformed symmetry is also discussed. Our construction can be used for systematic development of field theories in the deformed spaces. (orig.)

  19. Crossing symmetry in Alpha space

    CERN Multimedia

    CERN. Geneva

    2017-01-01

    The conformal bootstrap program aims to catalog all conformal field theories (second-order phase transitions) in D dimensions. Despite its ambitious scope much progress has been made over the past decade, e.g. in computing critical exponents for the 3D O(N) models to high precision. At this stage, analytic methods to explore the CFT landscape are not as well developed. In this talk I will describe a new mathematical framework for the bootstrap known as "alpha space", which reduces crossing symmetry to a set of integral equations. Based on arXiv:1702.08471 (with Balt van Rees) and arXiv:1703.08159.

  20. Unbounded representations of symmetry groups in gauge quantum field theory. Pt. 1

    International Nuclear Information System (INIS)

    Voelkel, A.H.

    1983-01-01

    Symmetry groups and especially the covariance (substitution rules) of the basic fields in a gauge quantum field theory of the Wightman-Garding type are investigated. By means of the continuity properties hidden in the substitution rules it is shown that every unbounded form-isometric representation U of a Lie group has a form-skew-symmetric differential deltaU with dense domain in the unphysical Hilbert space. Necessary and sufficient conditions for the existence of the closures of U and deltaU as well as for the isometry of U are derived. It is proved that a class of representations of the transition group enforces a relativistic confinement mechanism, by which some or all basic fields are confined but certain mixed products of them are not. (orig.)

  1. An electron diffraction and bond valence sum study of the space group symmetries and structures of the photocatalytic 1:1 ordered A2InNbO6 double perovskites (A=Ca2+, Sr2+, Ba2+)

    International Nuclear Information System (INIS)

    Ting, V.; Liu, Y.; Withers, R.L.; Krausz, E.

    2004-01-01

    A careful investigation has been carried out into the space group symmetries, structures and crystal chemistries of the 1:1 B-site ordered double perovskites A 2 InNbO 6 (A=Ca 2+ , Sr 2+ , Ba 2+ ) using a combination of bond valence sum calculations, powder XRD and electron diffraction. A recent investigation of these compounds by Yin et al. reported a random distribution of In 3+ and Nb 5+ ions onto the perovskite B-site positions of these compounds and hence Pm3-barm (a=a p , subscript p for parent perovskite sub-structure) space group symmetry for the A=Ba and Sr compounds and Pnma (a=a p +b p , b=-a p +b p , c=2c p ) space group symmetry for the A=Ca compound. A careful electron diffraction study, however, shows that both the A=Ca and Sr compounds occur at room temperature in P12 1 /n1 (a=a p +b p , b=-a p +b p , c=2c p ) perovskite-related superstructure phases while the A=Ba compound occurs in the Fm3-barm, a=2a p , elpasolite structure type. Bond valence sum calculations are used to explain why this should be so as well as to provide a useful first-order approximation to the structures of each of the compounds

  2. Comparison of the Cc and R3c space groups for the superlattice phase of Pb(Zr0.52Ti0.48)O3

    International Nuclear Information System (INIS)

    Ranjan, Rajeev; Singh, Akhilesh Kumar; Ragini; Pandey, Dhananjai

    2005-01-01

    Recent controversy about the space group of the low temperature superlattice phase of Pb(Zr 0.52 Ti 0.48 )O 3 is settled. It is shown that the R3c space group for the superlattice phase cannot correctly account for the peak positions of the superlattice reflections present in the neutron diffraction patterns. The correct space group is reconfirmed to be Cc. A comparison of the atomic coordinates of Cc and Cm space groups is also presented to show that in the absence of superlattice reflections, as is the case with x-ray diffraction data, one would land up in the Cm space group. This superlattice phase is found to coexist with another monoclinic phase of the Cm space group

  3. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  4. Hidden U$_{q}$(sl(2)) x U$_{q}$(sl(2)) quantum group symmetry in two dimensional gravity

    CERN Document Server

    Cremmer, E; Schnittger, J

    1997-01-01

    In a previous paper, we proposed a construction of U_q(sl(2)) quantum group symmetry generators for 2d gravity, where we took the chiral vertex operators of the theory to be the quantum group covariant ones established in earlier works. The basic idea was that the covariant fields in the spin 1/2 representation themselves can be viewed as generators, as they act, by braiding, on the other fields exactly in the required way. Here we transform this construction to the more conventional description of 2d gravity in terms of Bloch wave/Coulomb gas vertex operators, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2))\\otimes U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (bra/ket Verma-modules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of...

  5. Symmetry an introduction to group theory and its applications

    CERN Document Server

    McWeeny, Roy

    2002-01-01

    Well-organized volume develops ideas of group and representation theory in progressive fashion. Emphasis on finite groups describing symmetry of regular polyhedra and of repeating patterns, plus geometric illustrations.

  6. Additivity of Feature-based and Symmetry-based Grouping Effects in Multiple Object Tracking

    Directory of Open Access Journals (Sweden)

    Chundi eWang

    2016-05-01

    Full Text Available Multiple object tracking (MOT is an attentional process wherein people track several moving targets among several distractors. Symmetry, an important indicator of regularity, is a general spatial pattern observed in natural and artificial scenes. According to the laws of perceptual organization proposed by Gestalt psychologists, regularity is a principle of perceptual grouping, such as similarity and closure. A great deal of research reported that feature-based similarity grouping (e.g., grouping based on color, size, or shape among targets in MOT tasks can improve tracking performance. However, no additive feature-based grouping effects have been reported where the tracking objects had two or more features. Additive effect refers to a greater grouping effect produced by grouping based on multiple cues instead of one cue. Can spatial symmetry produce a similar grouping effect similar to that of feature similarity in MOT tasks? Are the grouping effects based on symmetry and feature similarity additive? This study includes four experiments to address these questions. The results of Experiments 1 and 2 demonstrated the automatic symmetry-based grouping effects. More importantly, an additive grouping effect of symmetry and feature similarity was observed in Experiments 3 and 4. Our findings indicate that symmetry can produce an enhanced grouping effect in MOT and facilitate the grouping effect based on color or shape similarity. The where and what pathways might have played an important role in the additive grouping effect.

  7. The geometric role of symmetry breaking in gravity

    International Nuclear Information System (INIS)

    Wise, Derek K

    2012-01-01

    In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry of the homogeneous space G/H. The deep reason for this is Cartan's 'method of equivalence,' giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.

  8. Chiral-symmetry breaking and confinement in Minkowski space

    Energy Technology Data Exchange (ETDEWEB)

    Biernat, Elmer P. [Unibersidade de Lisboa, 104-001, Lisboa, Portugal; Pena, M. T. [Universidade de Lisboa, 1049-001, Lisboa, Portugal; Ribiero, J. E. [Universidade de Lisboa, 1049-001 Lisboa, Portugal; Stadler, Alfred [Universidade de Évora, 7000-671 Évora, Portugal; Universidade de Lisboa, 1049-001 Lisboa, Portugal; Gross, Franz [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

    2016-01-01

    We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.

  9. Chiral-symmetry breaking and confinement in Minkowski space

    International Nuclear Information System (INIS)

    Biernat, Elmar P.; Peña, M. T.; Ribeiro, J. E.; Stadler, Alfred; Gross, Franz

    2016-01-01

    We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab

  10. Chiral-symmetry breaking and confinement in Minkowski space

    Energy Technology Data Exchange (ETDEWEB)

    Biernat, Elmar P. [Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Peña, M. T. [Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Departamento de Física, Instituto Superior Técnico (IST), Universidadede Lisboa, 1049-001 Lisboa (Portugal); Ribeiro, J. E. [Centro de Física das Interações Fundamentais (CFIF), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Stadler, Alfred [Departamento de Física, Universidade de Évora, 7000-671 Évora (Portugal); Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Gross, Franz [Thomas Jefferson National Accelerator Facility (JLab), Newport News, Virginia 23606 (United States)

    2016-01-22

    We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.

  11. Geometry and symmetry

    CERN Document Server

    Yale, Paul B

    2012-01-01

    This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

  12. Novel monoclinic zirconolite in Bi2O3–CuO–Ta2O5 ternary system: Phase equilibria, structural and electrical properties

    International Nuclear Information System (INIS)

    Tan, K.B.; Chon, M.P.; Khaw, C.C.; Zainal, Z.; Taufiq Yap, Y.H.; Tan, P.Y.

    2014-01-01

    Highlights: • Novel BCT monoclinic zirconolite phase was prepared through solid state reaction. • Comprehensive study of reaction mechanism was performed by careful firing control. • Qualitative structural and phase analyses were conducted. • Electrical response in broad range of temperature and frequency was investigated. - Abstract: Synthesis of novel monoclinic zirconolite, Bi 1.92 Cu 0.08 (Cu 0.3 Ta 0.7 ) 2 O 7.06 (β-BCT) using solid state reaction had been finalised at the firing temperature of 900 °C over 24 h. The X–ray diffraction pattern of β-BCT was fully indexed on a monoclinic symmetry, space group, C2/c with lattice constants, a = 13.1052 (8), b = 7.6749 (5), c = 12.162 (6), α = γ = 90° and β = 101.32° (1), respectively. The reaction mechanism study indicated phase formation was greatly influenced by the reaction between intermediate bismuth tantalate binary phases and CuO at elevated temperatures. β-BCT was thermally stable up to a temperature of 900 °C and contained spherulite grains with sizes ranging from 1 to 14 μm. Electrical properties of this material were characterised over a broad temperature range covering temperatures from 10 K to 874 K. At the temperature of 304 K, two semicircles were discernible in complex Cole–Cole plot showing an insulating grain boundary with C gb = 6.63 × 10 −9 F cm −1 and a bulk response capacitance, C b = 6.74 × 10 −12 F cm −1 . The Power law frequency-dependent ac conductivity of β-BCT was apparent in three frequency regimes; a low–frequency plateau regime, a high-frequency plateau regime and a dispersive regime taking place in the temperature range of 220–576 K. The frequency-dependent ac conductivity of β-BCT with increasing temperature was attributed to the thermal activated electrical conduction mechanism within the structure

  13. EXECUTIVE SUMMARY OF THE SNOWMASS 2001 WORKING GROUP : ELECTROWEAK SYMMETRY BREAKING

    International Nuclear Information System (INIS)

    CARENA, M.; GERDES, D.W.; HABER, H.E.; TURCOT, A.S.; ZERWAS, P.M.

    2001-01-01

    In this summary report of the 2001 Snowmass Electroweak Symmetry Breaking Working Group, the main candidates for theories of electroweak symmetry breaking are surveyed, and the criteria for distinguishing among the different approaches are discussed. The potential for observing electroweak symmetry breaking phenomena at the upgraded Tevatron and the LHC is described. We emphasize the importance of a high-luminosity e + e - linear collider for precision measurements to clarify the underlying electroweak symmetry breaking dynamics. Finally, we note the possible roles of the μ + μ - collider and VLHC for further elucidating the physics of electroweak symmetry breaking

  14. Operational symmetries basic operations in physics

    CERN Document Server

    Saller, Heinrich

    2017-01-01

    This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato’s and Kepler’s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups an...

  15. Gauge origin of discrete flavor symmetries in heterotic orbifolds

    Directory of Open Access Journals (Sweden)

    Florian Beye

    2014-09-01

    Full Text Available We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kähler modulus T. Using this mechanism it is shown that the Δ(54 non-Abelian discrete symmetry group originates from a SU(3 gauge symmetry, whereas the D4 symmetry group is obtained from a SU(2 gauge symmetry.

  16. Symmetry gauge theory for paraparticles

    International Nuclear Information System (INIS)

    Kursawe, U.

    1986-01-01

    In the present thesis it was shown that for identical particles the wave function of which has a more complicated symmetry than it is the case at the known kinds of particles, the bosons and fermions, a gauge theory can be formulated, the so-called 'symmetry gauge theory'. This theory has its origin alone in the symmetry of the particle wave functions and becomes first relevant when more than two particles are considered. It was shown that for particles with mixed-symmetrical wave functions, so-called 'paraparticles', the quantum mechanical state is no more described by one Hilbert-space element but by a many-dimensional subspace of this Hilbert space. The gauge freedom consists then just in the freedom of the choice of the basis in this subspace, the corresponding gauge group is the group of the unitary basis transformation in this subspace. (orig./HSI) [de

  17. Symmetries and groups in particle physics; Symmetrien und Gruppen in der Teilchenphysik

    Energy Technology Data Exchange (ETDEWEB)

    Scherer, Stefan [Mainz Univ. (Germany)

    2016-07-01

    The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to

  18. Quantum symmetry in quantum theory

    International Nuclear Information System (INIS)

    Schomerus, V.

    1993-02-01

    Symmetry concepts have always been of great importance for physical problems like explicit calculations, classification or model building. More recently, new 'quantum symmetries' ((quasi) quantum groups) attracted much interest in quantum theory. It is shown that all these quantum symmetries permit a conventional formulation as symmetry in quantum mechanics. Symmetry transformations can act on the Hilbert space H of physical states such that the ground state is invariant and field operators transform covariantly. Models show that one must allow for 'truncation' in the tensor product of representations of a quantum symmetry. This means that the dimension of the tensor product of two representations of dimension σ 1 and σ 2 may be strictly smaller than σ 1 σ 2 . Consistency of the transformation law of field operators local braid relations leads us to expect, that (weak) quasi quantum groups are the most general symmetries in local quantum theory. The elements of the R-matrix which appears in these local braid relations turn out to be operators on H in general. It will be explained in detail how examples of field algebras with weak quasi quantum group symmetry can be obtained. Given a set of observable field with a finite number of superselection sectors, a quantum symmetry together with a complete set of covariant field operators which obey local braid relations are constructed. A covariant transformation law for adjoint fields is not automatic but will follow when the existence of an appropriate antipode is assumed. At the example of the chiral critical Ising model, non-uniqueness of the quantum symmetry will be demonstrated. Generalized quantum symmetries yield examples of gauge symmetries in non-commutative geometry. Quasi-quantum planes are introduced as the simplest examples of quasi-associative differential geometry. (Weak) quasi quantum groups can act on them by generalized derivations much as quantum groups do in non-commutative (differential-) geometry

  19. Group symmetries and information propagation

    International Nuclear Information System (INIS)

    Draayer, J.P.

    1980-01-01

    Spectroscopy concerns itself with the ways in which the Hamiltonian and other interesting operators defined in few-particle spaces are determined or determine properties of many-particle systems. But the action of the central limit theorem (CLT) filters the transmission of information between source and observed so whether propagating forward from a few-particle defining space, as is usual in theoretical studies, or projecting backward to it from measured things, each is only sensitive to averaged properties of the other. Our concern is with the propagation of spectroscopic information in the presence of good symmetries when filtering action of the CLT is effective. Specifically, we propose to address the question, What propagates and how. We begin with some examples, using both scalar and isospin geometries to illustrate simple propagation. Examples of matrix propagation are studied; contact with standard tensor algebra is established and an algorithm put forward for the expansion of any operator in terms of another set, complete or not; shell-model results for 20 Ne using a realistic interaction and two trace-equivalent forms are presented; and some further challenges are mentioned

  20. Recursions of Symmetry Orbits and Reduction without Reduction

    Directory of Open Access Journals (Sweden)

    Andrei A. Malykh

    2011-04-01

    Full Text Available We consider a four-dimensional PDE possessing partner symmetries mainly on the example of complex Monge-Ampère equation (CMA. We use simultaneously two pairs of symmetries related by a recursion relation, which are mutually complex conjugate for CMA. For both pairs of partner symmetries, using Lie equations, we introduce explicitly group parameters as additional variables, replacing symmetry characteristics and their complex conjugates by derivatives of the unknown with respect to group parameters. We study the resulting system of six equations in the eight-dimensional space, that includes CMA, four equations of the recursion between partner symmetries and one integrability condition of this system. We use point symmetries of this extended system for performing its symmetry reduction with respect to group parameters that facilitates solving the extended system. This procedure does not imply a reduction in the number of physical variables and hence we end up with orbits of non-invariant solutions of CMA, generated by one partner symmetry, not used in the reduction. These solutions are determined by six linear equations with constant coefficients in the five-dimensional space which are obtained by a three-dimensional Legendre transformation of the reduced extended system. We present algebraic and exponential examples of such solutions that govern Legendre-transformed Ricci-flat Kähler metrics with no Killing vectors. A similar procedure is briefly outlined for Husain equation.

  1. On the labeling and symmetry adaptation of the solvable finite groups representations

    International Nuclear Information System (INIS)

    Caride, A.O.; Zanette, S.I.; Nogueira, S.R.A.

    1987-01-01

    We propose a method to simultaneously perform a symmetry adaptation and a labeling of the bases of the irreducible representations of the solvable finite groups. It is performed by difining a self-adjoint operator with ligenvalues which evidence the descent in symmetry of the group-subgroups sequences. We also prove two theorems on the canonicity of the cpomposition series of the solvable groups. (author) [pt

  2. Group theoretical symmetries and generalized Bäcklund transformations for integrable systems

    Science.gov (United States)

    Haak, Guido

    1994-05-01

    A notion of symmetry for 1+1-dimensional integrable systems is presented which is consistent with their group theoretic description. It is shown how a group symmetry may be used together with a dynamical reduction to produce new generalizations of the Bäcklund transformation for the Korteweg-de Vries equation to its SL(n,C) generalization. An additional application to the relativistic invariance of the Leznov-Saveliev systems is given.

  3. Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity

    Directory of Open Access Journals (Sweden)

    Fraser Halley

    2011-05-01

    Full Text Available Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classified into one of 17 different Wallpaper groups, and while computational models have been developed which can extract an image's symmetry group, very little work has been done on how humans perceive these patterns. This study presents the results from a grouping experiment using stimuli from the different wallpaper groups. We find that while different images from the same wallpaper group are perceived as similar to one another, not all groups have the same degree of self-similarity. The similarity relationships between wallpaper groups appear to be dominated by rotations.

  4. Higgsless theory of electroweak symmetry breaking from warped space

    International Nuclear Information System (INIS)

    Nomura, Yasunori

    2003-01-01

    We study a theory of electroweak symmetry breaking without a Higgs boson, recently suggested by Csaki et al. The theory is formulated in 5D warped space with the gauge bosons and matter fields propagating in the bulk. In the 4D dual picture, the theory appears as the standard model without a Higgs field, but with an extra gauge group G which becomes strong at the TeV scale. The strong dynamics of G breaks the electroweak symmetry, giving the masses for the W and Z bosons and the quarks and leptons. We study corrections in 5D which are logarithmically enhanced by the large mass ratio between the Planck and weak scales, and show that they do not destroy the structure of the electroweak gauge sector at the leading order. We introduce a new parameter, the ratio between the two bulk gauge couplings, into the theory and find that it allows us to control the scale of new physics. We also present a potentially realistic theory accommodating quarks and leptons and discuss its implications, including the violation of universality in the W and Z boson couplings to matter and the spectrum of the Kaluza-Klein excitations of the gauge bosons. The theory reproduces many successful features of the standard model, although some cancellations may still be needed to satisfy constraints from the precision electroweak data. (author)

  5. Quantum symmetries of classical spaces

    OpenAIRE

    Bhowmick, Jyotishman; Goswami, Debashish; Roy, Subrata Shyam

    2009-01-01

    We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^*$ algebra) compact quantum groups on classical topological spaces. Using this, we show that: (i) a compact connected classical space can have a faithful action by a genuine compact quantum group, and (ii) there exists a spectral triple on a classical connected compact space for which the quantum group of orientation and volume preserving isometries (in the sense of \\cite{qorient}) is a genuine quantum...

  6. Surveying the quantum group symmetries of integrable open spin chains

    Science.gov (United States)

    Nepomechie, Rafael I.; Retore, Ana L.

    2018-05-01

    Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A2n(2), A2n-1 (2) , Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of g ˆ . We show that these transfer matrices also have a duality symmetry (for the cases Cn(1) and Dn(1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n-1 (2) , Bn(1) and Dn(1)). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

  7. Detection and correction of underassigned rotational symmetry prior to structure deposition

    International Nuclear Information System (INIS)

    Poon, Billy K.; Grosse-Kunstleve, Ralf W.; Zwart, Peter H.; Sauter, Nicholas K.

    2010-01-01

    An X-ray structural model can be reassigned to a higher symmetry space group using the presented framework if its noncrystallographic symmetry operators are close to being exact crystallographic relationships. About 2% of structures in the Protein Data Bank can be reclassified in this way. Up to 2% of X-ray structures in the Protein Data Bank (PDB) potentially fit into a higher symmetry space group. Redundant protein chains in these structures can be made compatible with exact crystallographic symmetry with minimal atomic movements that are smaller than the expected range of coordinate uncertainty. The incidence of problem cases is somewhat difficult to define precisely, as there is no clear line between underassigned symmetry, in which the subunit differences are unsupported by the data, and pseudosymmetry, in which the subunit differences rest on small but significant intensity differences in the diffraction pattern. To help catch symmetry-assignment problems in the future, it is useful to add a validation step that operates on the refined coordinates just prior to structure deposition. If redundant symmetry-related chains can be removed at this stage, the resulting model (in a higher symmetry space group) can readily serve as an isomorphous replacement starting point for re-refinement using re-indexed and re-integrated raw data. These ideas are implemented in new software tools available at http://cci.lbl.gov/labelit

  8. Bogolyubov renormalization group and symmetry of solution in mathematical physics

    International Nuclear Information System (INIS)

    Shirkov, D.V.; Kovalev, V.F.

    2000-01-01

    Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparametrization one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of a new approach to solution for a problem of self-focusing laser beam in a nonlinear medium

  9. Noncompact symmetries in string theory

    International Nuclear Information System (INIS)

    Maharana, J.; Schwarz, J.H.

    1993-01-01

    Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by noncompact groups modded out by their maximal compact subgroups and discrete duality groups. Then it was found that many other moduli spaces have analogous descriptions. More recently, noncompact group symmetries have turned up in effective actions used to study string cosmology and other classical configurations. This paper explores these noncompact groups in the case of toroidal compactification both from the viewpoint of low-energy effective field theory, using the method of dimensional reduction, and from the viewpoint of the string theory world-sheet. The conclusion is that all these symmetries are intimately related. In particular, we find that Chern-Simons terms in the three-form field strength H μνρ play a crucial role. (orig.)

  10. Description of symmetry of magnetic structures by representations of space groups. [Tables, projecton operator methods

    Energy Technology Data Exchange (ETDEWEB)

    Sikora, W

    1974-10-15

    A description of magnetic structures based on the use of representations of space groups is given. Representations of the space groups were established for each compound on the basis of experimental data by the method of projection operators. The compounds contained in the list are collected according to crystal systems, alphabetically within each system. The description of each compound consists of the four parts. The first part contain the chemical symbol of the compound, the second its space group. The next part contains the chemical symbol of the magnetic atom and its positions in Wychoff notation with the number of equivalent positions in the crystal unit cell. The main description of a compound magnetic structure is given in the fourth part. It contains: K vector defined in the reciprocal space, the representation according to which a magnetic structure is transformed and the axial vector function S which describes the magnetic structure.

  11. Antiunitary symmetry operators in quantum mechanics

    International Nuclear Information System (INIS)

    Carinena, J.F.; Santander, M.

    1981-01-01

    A criterion to decide that some symmetries of a quantum system must be realized as antiunitary operators is given. It is based on some mathematical theorems about the second cohomology group of the symmetry group when expressed in terms of those of a normal subgroup and the corresponding factor group. It is also shown that this criterion implies that the only possibility for the unitary subgroup in the Galilean case is that generated by the space reflection and the connected component containing the identity; otherwise only massless systems would arise. (author)

  12. Grain size dependent phase stabilities and presence of a monoclinic (Pm) phase in the MPB region of (1-x)Bi(Mg_1_/_2Ti_1_/_2)O_3_-_xPbTiO_3

    International Nuclear Information System (INIS)

    Upadhyay, A.; Singh, A.K.

    2016-01-01

    The results of the room temperature structural studies on (1-x)Bi(Mg_1_/_2Ti_1_/_2)O_3_-_xPbTiO_3 ceramics using Rietveld analysis of the powder X-ray diffraction data in the composition range 0.28≤x≤0.45 are presented. The morphotropic phase boundary region exhibits coexistence of monoclinic (space group Pm) and tetragonal (space group P4mm) phases in the composition range 0.33≤x≤0.40. The structure is nearly single phase monoclinic (space group Pm) in the composition range 0.28≤x≤0.32. The structure for the compositions with x≥0.45 is found to be predominantly tetragonal with space group P4mm. Rietveld refinement of the structure rules out the coexistence of rhombohedral and tetragonal phases in the morphotropic phase boundary region reported by earlier authors. The Rietveld structure analysis for the sample x=0.35 calcined at various temperatures reveals that phase fraction of the coexisting phases in the morphotropic phase boundary region varies with grain size. The structural parameters of the two coexisting phases also change slightly with changing grain size. (author)

  13. Symmetries, Information and Monster Groups before and after the Big Bang

    Directory of Open Access Journals (Sweden)

    Arturo Tozzi

    2016-12-01

    Full Text Available The Monster group, the biggest of the sporadic groups, is equipped with the highest known number of dimensions and symmetries. Taking into account variants of the Borsuk–Ulam theorem and a novel topological approach cast in a physical fashion that has the potential to be operationalized, the universe can be conceived as a lower-dimensional manifold encompassed in the Monster group. Our universe might arise from spontaneous dimension decrease and symmetry breaking that occur inside the very structure of the Monster Module. We elucidate how the energetic loss caused by projection from higher to lower dimensions and by the Monster group’s non-abelian features is correlated with the present-day asymmetry in the thermodynamic arrow. By linking the Monster Module to its theoretical physical counterparts, it is then possible to calculate its enthalpy and Lie group trajectories. Our approach also reveals how a symmetry break might lead to a universe based on multi-dimensional string theories and CFT/AdS (anti-de Sitter/conformal field theory correspondence.

  14. Non-linear entropy functionals and a characteristic invariant of symmetry group actions on infinite quantum systems

    International Nuclear Information System (INIS)

    Hudetz, T.

    1989-01-01

    We review the development of the non-Abelian generalization of the Kolmogorov-Sinai(KS) entropy invariant, as initated by Connes and Stormer and completed by Connes, Narnhofer and Thirring only recently. As an introduction and motivation, the classical KS theory is reformulated in terms of Abelian W * -algebras. Finally, we describe simple physical applications of the developed characteristic invariant to space-time symmetry group actions on infinite quantum systems. 42 refs. (Author)

  15. Novel monoclinic zirconolite in Bi{sub 2}O{sub 3}–CuO–Ta{sub 2}O{sub 5} ternary system: Phase equilibria, structural and electrical properties

    Energy Technology Data Exchange (ETDEWEB)

    Tan, K.B., E-mail: tankb@science.upm.my [Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor (Malaysia); Chon, M.P. [Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor (Malaysia); Khaw, C.C. [Department of Mechanical and Material Engineering, Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, 53300 Setapak, Kuala Lumpur (Malaysia); Zainal, Z.; Taufiq Yap, Y.H.; Tan, P.Y. [Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor (Malaysia)

    2014-04-01

    Highlights: • Novel BCT monoclinic zirconolite phase was prepared through solid state reaction. • Comprehensive study of reaction mechanism was performed by careful firing control. • Qualitative structural and phase analyses were conducted. • Electrical response in broad range of temperature and frequency was investigated. - Abstract: Synthesis of novel monoclinic zirconolite, Bi{sub 1.92}Cu{sub 0.08}(Cu{sub 0.3}Ta{sub 0.7}){sub 2}O{sub 7.06} (β-BCT) using solid state reaction had been finalised at the firing temperature of 900 °C over 24 h. The X–ray diffraction pattern of β-BCT was fully indexed on a monoclinic symmetry, space group, C2/c with lattice constants, a = 13.1052 (8), b = 7.6749 (5), c = 12.162 (6), α = γ = 90° and β = 101.32° (1), respectively. The reaction mechanism study indicated phase formation was greatly influenced by the reaction between intermediate bismuth tantalate binary phases and CuO at elevated temperatures. β-BCT was thermally stable up to a temperature of 900 °C and contained spherulite grains with sizes ranging from 1 to 14 μm. Electrical properties of this material were characterised over a broad temperature range covering temperatures from 10 K to 874 K. At the temperature of 304 K, two semicircles were discernible in complex Cole–Cole plot showing an insulating grain boundary with C{sub gb} = 6.63 × 10{sup −9} F cm{sup −1} and a bulk response capacitance, C{sub b} = 6.74 × 10{sup −12} F cm{sup −1}. The Power law frequency-dependent ac conductivity of β-BCT was apparent in three frequency regimes; a low–frequency plateau regime, a high-frequency plateau regime and a dispersive regime taking place in the temperature range of 220–576 K. The frequency-dependent ac conductivity of β-BCT with increasing temperature was attributed to the thermal activated electrical conduction mechanism within the structure.

  16. The analysis of crystallographic symmetry types in finite groups

    Science.gov (United States)

    Sani, Atikah Mohd; Sarmin, Nor Haniza; Adam, Nooraishikin; Zamri, Siti Norziahidayu Amzee

    2014-06-01

    Undeniably, it is human nature to prefer objects which are considered beautiful. Most consider beautiful as perfection, hence they try to create objects which are perfectly balance in shape and patterns. This creates a whole different kind of art, the kind that requires an object to be symmetrical. This leads to the study of symmetrical objects and pattern. Even mathematicians and ethnomathematicians are very interested with the essence of symmetry. One of these studies were conducted on the Malay traditional triaxial weaving culture. The patterns derived from this technique are symmetrical and this allows for further research. In this paper, the 17 symmetry types in a plane, known as the wallpaper groups, are studied and discussed. The wallpaper groups will then be applied to the triaxial patterns of food cover in Malaysia.

  17. Scale symmetry and virial theorem

    International Nuclear Information System (INIS)

    Westenholz, C. von

    1978-01-01

    Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework

  18. PL-1 program system for generalized Patterson superpositions. [PL1GEN, SYMPL1, and ALSPL1, in PL/1 for IBM 360/65 computer

    Energy Technology Data Exchange (ETDEWEB)

    Hubbard, C.R.; Babich, M.W.; Jacobson, R.A.

    1977-01-01

    A new system of three programs written in PL/1 can calculate symmetry and Patterson superposition maps for triclinic, monoclinic, and orthorhombic space groups as well as any space group reducible to one of these three. These programs are based on a system of FORTRAN programs developed at Ames Laboratory, but are more general and have expanded utility, especially with regard to large unit cells. The program PLIGEN calculates a direct access data set, SYMPL1 calculates a direct access symmetry map, and ALSPL1 calculates a superposition map using one or multiple superpositions. A detailed description of the use of these programs including symbolic program listings is included. 2 tables.

  19. 2-(4-Fluorobenzylidenepropanedinitrile: monoclinic polymorph

    Directory of Open Access Journals (Sweden)

    Ahmed M. El-Agrody

    2013-04-01

    Full Text Available The title compound, C10H5FN2, is a monoclinic (P21/c polymorph of the previously reported triclinic (P-1 form [Antipin et al. (2003. J. Mol. Struct. 650, 1–20]. The 13 non-H atoms in the title polymorph are almost coplanar (r.m.s. deviation = 0.020 Å; a small twist between the fluorobenzene and dinitrile groups [C—C—C—C torsion angle = 175.49 (16°] is evident in the triclinic polymorph. In the crystal, C—H...N interactions lead to supramolecular layers parallel to (-101; these are connected by C—F...π interactions.

  20. Symmetry witnesses

    Science.gov (United States)

    Aniello, Paolo; Chruściński, Dariusz

    2017-07-01

    A symmetry witness is a suitable subset of the space of selfadjoint trace class operators that allows one to determine whether a linear map is a symmetry transformation, in the sense of Wigner. More precisely, such a set is invariant with respect to an injective densely defined linear operator in the Banach space of selfadjoint trace class operators (if and) only if this operator is a symmetry transformation. According to a linear version of Wigner’s theorem, the set of pure states—the rank-one projections—is a symmetry witness. We show that an analogous result holds for the set of projections with a fixed rank (with some mild constraint on this rank, in the finite-dimensional case). It turns out that this result provides a complete classification of the sets of projections with a fixed rank that are symmetry witnesses. These particular symmetry witnesses are projectable; i.e. reasoning in terms of quantum states, the sets of ‘uniform’ density operators of corresponding fixed rank are symmetry witnesses too.

  1. Some New Lie Symmetry Groups of Differential-Difference Equations Obtained from a Simple Direct Method

    International Nuclear Information System (INIS)

    Zhi Hongyan

    2009-01-01

    In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen-Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.

  2. Constraining the physical state by symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Fatibene, L., E-mail: lorenzo.fatibene@unito.it [Department of Mathematics, University of Torino (Italy); INFN - Sezione Torino - IS QGSKY (Italy); Ferraris, M.; Magnano, G. [Department of Mathematics, University of Torino (Italy)

    2017-03-15

    After reviewing the hole argument and its relations with initial value problem and general covariance, we shall discuss how much freedom one has to define the physical state in a generally covariant field theory (with or without internal gauge symmetries). Our analysis relies on Cauchy problems, thus it is restricted to globally hyperbolic spacetimes. We shall show that in generally covariant theories on a compact space (as well as for internal gauge symmetries on any spacetime) one has no freedom and one is forced to declare as physically equivalent two configurations which differ by a global spacetime diffeomorphism (or by an internal gauge transformation) as it is usually prescribed. On the contrary, when space is not compact, the result does not hold true and one may have different options to define physically equivalent configurations, still preserving determinism. - Highlights: • Investigate the relation between the hole argument, covariance, determinism and physical state. • Show that if space is compact then any diffeomorphism is a gauge symmetry. • Show that if space is not compact then there may be more freedom in choosing gauge group.

  3. Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

    Science.gov (United States)

    Ahn, Junyeong; Yang, Bohm-Jung

    2017-04-01

    We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

  4. Computing the Symmetry Groups of the Platonic Solids With the ...

    Indian Academy of Sciences (India)

    group theory and use of the computer algebra package. Maple. The five platonic solids are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosa- hedron. By determining a symmetry group, we lllean not just to determine its elements but to identify it, up to isomorphism, with a well-known group, such as ...

  5. Symmetry breaking patterns for inflation

    Science.gov (United States)

    Klein, Remko; Roest, Diederik; Stefanyszyn, David

    2018-06-01

    We study inflationary models where the kinetic sector of the theory has a non-linearly realised symmetry which is broken by the inflationary potential. We distinguish between kinetic symmetries which non-linearly realise an internal or space-time group, and which yield a flat or curved scalar manifold. This classification leads to well-known inflationary models such as monomial inflation and α-attractors, as well as a new model based on fixed couplings between a dilaton and many axions which non-linearly realises higher-dimensional conformal symmetries. In this model, inflation can be realised along the dilatonic direction, leading to a tensor-to-scalar ratio r ˜ 0 .01 and a spectral index n s ˜ 0 .975. We refer to the new model as ambient inflation since inflation proceeds along an isometry of an anti-de Sitter ambient space-time, which fully determines the kinetic sector.

  6. Symmetries and nuclei

    International Nuclear Information System (INIS)

    Henley, E.M.

    1987-01-01

    Nuclei are very useful for testing symmetries, and for studies of symmetry breaking. This thesis is illustrated for two improper space-time transformations, parity and time-reversal and for one internal symmetry: charge symmetry and independence. Recent progress and present interest is reviewed. 23 refs., 8 figs., 2 tabs

  7. Symmetry and symmetry breaking in quantum mechanics

    International Nuclear Information System (INIS)

    Chomaz, Philippe

    1998-01-01

    In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels us of thinking the Single to comprehend the Universal. Quantum Numbers, magic Numbers and Numbers sign the wave. The matter is vibration. To describe the music of the world one needs keys, measures, notes, rules and partition: one needs quantum mechanics. The particles reduce themselves not in material points as the scholars of the past centuries thought, but they must be conceived throughout the space, in the accomplishment of shapes of volumes. When Einstein asked himself whether God plays dice, there was no doubt among its contemporaries that if He exists He is a geometer. In a Nature reduced to Geometry, the symmetries assume their role in servicing the Harmony. The symmetries allow ordering the energy levels to make them understandable. They impose there geometrical rules to the matter waves, giving them properties which sometimes astonish us. Hidden symmetries, internal symmetries and newly conceived symmetries have to be adopted subsequently to the observation of some order in this world of Quanta. In turn, the symmetries provide new observables which open new spaces of observation

  8. A re-examination of symmetry/Group relationships as applied ot the elementary particles

    International Nuclear Information System (INIS)

    Byrd, K.; Cole R.

    1993-01-01

    The purpose of this investigation is to apply Group Theory to the elementary particles. Group Theory is a mathematical discipline used to predict the existence of elementary particles by physicists. Perhaps, the most famous application of Group Theory to the elementary particles was by Murray Gell-Mann in 1964. Gell-Mann used the theory to predict the existence and characteristics of the then undiscovered Omega Minus Particle. Group Theory relies heavily on symmetry relationships and expresses them in terms of geometry. Existence and the characteristics of a logical intuitable, but unobserved member of a group are given by extrapolation of the geometric relationships and characteristics of the known members of the group. In this study, the Delta, Sigma, Chi and Omega baryons are used to illustrate how physicists apply geometry and symmetrical relationships to predict new particles. The author's hypothesis is that by using the D3 crystal symmetry group and Gell-Mann's baryons, three new particles will be predicted. The results of my new symmetry predicts the Omega 2, Omega 3, and Chi 3. However, the Chi 3 does not have characteristics consistent with those of the other known group members

  9. Symmetries and microscopic physics

    International Nuclear Information System (INIS)

    Blaizot, J.P.

    1997-01-01

    This book is based on a course of lectures devoted to the applications of group theory to quantum physics. The purpose is to give students a precise idea of general principles involving the concept of symmetry and to present practical methods used to calculate physical properties derived from symmetries. The first chapter is an introduction to the main results of group theory, 2 chapters highlight principles and methods concerning geometrical transformations in the space of states, state degeneracy and perturbation theory. The last 4 chapters investigate the applications of these methods to atom physics, nuclear structure and elementary particles. A chapter is devoted to the atom of hydrogen and another to the isospin. Numerous exercises and problems, some with their corrections, are proposed. (A.C.)

  10. On standardization of low symmetry crystal fields

    Science.gov (United States)

    Gajek, Zbigniew

    2015-07-01

    Standardization methods of low symmetry - orthorhombic, monoclinic and triclinic - crystal fields are formulated and discussed. Two alternative approaches are presented, the conventional one, based on the second-rank parameters and the standardization based on the fourth-rank parameters. Mainly f-electron systems are considered but some guidelines for d-electron systems and the spin Hamiltonian describing the zero-field splitting are given. The discussion focuses on premises for choosing the most suitable method, in particular on inadequacy of the conventional one. Few examples from the literature illustrate this situation.

  11. Symmetry and physical properties of crystals

    CERN Document Server

    Malgrange, Cécile; Schlenker, Michel

    2014-01-01

    Crystals are everywhere, from natural crystals (minerals) through the semiconductors and magnetic materials in electronic devices and computers or piezoelectric resonators at the heart of our quartz watches to electro-optical devices. Understanding them in depth is essential both for pure research and for their applications. This book provides a clear, thorough presentation of their symmetry, both at the microscopic space-group level and the macroscopic point-group level. The implications of the symmetry of crystals for their physical properties are then presented, together with their mathematical description in terms of tensors. The conditions on the symmetry of a crystal for a given property to exist then become clear, as does the symmetry of the property. The geometrical representation of tensor quantities or properties is presented, and its use in determining important relationships emphasized. An original feature of this book is that most chapters include exercises with complete solutions. This all...

  12. Black Hole Entropy from Bondi-Metzner-Sachs Symmetry at the Horizon.

    Science.gov (United States)

    Carlip, S

    2018-03-09

    Near the horizon, the obvious symmetries of a black hole spacetime-the horizon-preserving diffeomorphisms-are enhanced to a larger symmetry group with a three-dimensional Bondi-Metzner-Sachs algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry and show that it is strong enough to determine the black hole entropy in any dimension.

  13. Discrete symmetries and their stringy origin

    International Nuclear Information System (INIS)

    Mayorga Pena, Damian Kaloni

    2014-05-01

    Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to R-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the Z 2 x Z 4 orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard Z 2 matter parity of the MSSM.

  14. Gauge fields in nonlinear group realizations involving two-dimensional space-time symmetry

    International Nuclear Information System (INIS)

    Machacek, M.E.; McCliment, E.R.

    1975-01-01

    It is shown that gauge fields may be consistently introduced into a model Lagrangian previously considered by the authors. The model is suggested by the spontaneous breaking of a Lorentz-type group into a quasiphysical two-dimensional space-time and one internal degree of freedom, loosely associated with charge. The introduction of zero-mass gauge fields makes possible the absorption via the Higgs mechanism of the Goldstone fields that appear in the model despite the fact that the Goldstone fields do not transform as scalars. Specifically, gauge invariance of the Yang-Mills type requires the introduction of two sets of massless gauge fields. The transformation properties in two-dimensional space-time suggest that one set is analogous to a charge doublet that behaves like a second-rank tensor in real four-dimensional space time. The other set suggests a spin-one-like charge triplet. Via the Higgs mechanism, the first set absorbs the Goldstone fields and acquires mass. The second set remains massless. If massive gauge fields are introduced, the associated currents are not conserved and the Higgs mechanism is no longer fully operative. The Goldstone fields are not eliminated, but coupling between the Goldstone fields and the gauge fields does shift the mass of the antisymmetric second-rank-tensor gauge field components

  15. On the representation of symmetry group transformation operators in the interaction picture

    International Nuclear Information System (INIS)

    Jorjadze, G.P.; Khvedelidze, A.M.; Kvinikhidze, A.H.

    1987-01-01

    The representation similar to that of Dyson, is obtained in the form of a chronologically (antichronologically) ordered exponent for operators of any symmetry group transformations of an interacting quantum field system. The exponent is given by an integral of the interaction Hamiltonian density in Dirac's picture. The domain of integration is determined by the symmetry transformation considered. 3 refs.; 2 figs

  16. The symmetries of magnetic structures in rare earth tetraborides

    International Nuclear Information System (INIS)

    Schaefer, W.; Will, G.; Buschow, K.H.J.

    1975-01-01

    The collinear antiferromagnetic spin configurations, which are possible in the rare earth tetraboride structure (space group P 4/mbm) and their distinction by neutron diffraction are discussed. The symmetries of the different antiferromagnetic structures are described by the corrosponding magnetic space groups. Neutron diffraction data collected from ErB 4 are integrated in the structure discussion. (orig.) [de

  17. Broken dynamical symmetries in quantum mechanics and phase transition phenomena

    International Nuclear Information System (INIS)

    Guenther, N.J.

    1979-12-01

    This thesis describes applications of dynamical symmetries to problems in quantum mechanics and many-body physics where the latter is formulated as a Euclidean scalar field theory in d-space dimensions. By invoking the concept of a dynamical symmetry group a unified understanding of apparently disparate results is achieved. (author)

  18. Symmetry, stability, and diffraction properties of icosahedral crystals

    International Nuclear Information System (INIS)

    Bak, P.

    1985-01-01

    In a remarkable experiment on an Mn-Al alloy, Shechtman et al. observed a diffraction spectrum with icosahedral symmetry. This is inconsistent with discrete translational invariance since the symmetry includes a five-fold axis. In this paper, it is shown that the crystallography and diffraction pattern can be described by a six-dimensional space group. The crystal structure in 3d is obtained as a cut along a 3d hyperplane in a regular 6d crystal. Displacements of the 6d crystal along 6 orthogonal directions define 6 continuous symmetries for the icosahedral crystal, three of which are phase symmetries describing internal rearrangements of the atoms

  19. Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space

    International Nuclear Information System (INIS)

    Leverrier, A; Karpov, E; Cerf, N J; Grangier, P

    2009-01-01

    Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.

  20. Gauge symmetries, topology, and quantisation

    International Nuclear Information System (INIS)

    Balachandran, A.P.

    1994-01-01

    The following two loosely connected sets of topics are reviewed in these lecture notes: (1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. (2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under (1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under (2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem

  1. Study of spontaneously broken conformal symmetry in curved space-times

    International Nuclear Information System (INIS)

    Janson, M.M.

    1977-05-01

    Spontaneous breakdown of Weyl invariance (local scale invariance) in a conformally-invariant extension of a gauge model for weak and electromagnetic interactions is considered. The existence of an asymmetric vacuum for the Higgs field, phi, is seen to depend on the space-time structure via the Gursey-Penrose term, approximately phi + phi R, in the action. (R denotes the scalar curvature.) The effects of a prescribed space-time structure on spontaneously broken Weyl invariance is investigated. In a cosmological space-time, it is found that initially, in the primordial fireball, the symmetry must hold exactly. Spontaneous symmetry breaking (SSB) develops as the universe expands and cools. Consequences of this model include a dependence of G/sub F/, the effective weak interaction coupling strength, on ''cosmic time.'' It is seen to decrease monotonically; in the present epoch (G/sub F//G/sub F/)/sub TODAY/ approximately less than 10 -10 (year) -1 . The effects of the Schwarzschild geometry on SSB are explored. In the interior of a neutron star the Higgs vacuum expectation value, and consequently G/sub F/, is found to have a radial dependence. The magnitude of this variation does not warrant revision of present models of neutron star structures. Another perspective on the problem considered a theory of gravitation (conformal relativity) to be incorporated in the conformally invariant gauge model of weak and electromagnetic interactions. If SSB develops, the vacuum gravitational field equations are the Einstein field equations with a cosmological constant. The stability of the asymmetric vacuum solution is investigated to ascertain whether SSB can occur

  2. An introduction to data reduction: space-group determination, scaling and intensity statistics.

    Science.gov (United States)

    Evans, Philip R

    2011-04-01

    This paper presents an overview of how to run the CCP4 programs for data reduction (SCALA, POINTLESS and CTRUNCATE) through the CCP4 graphical interface ccp4i and points out some issues that need to be considered, together with a few examples. It covers determination of the point-group symmetry of the diffraction data (the Laue group), which is required for the subsequent scaling step, examination of systematic absences, which in many cases will allow inference of the space group, putting multiple data sets on a common indexing system when there are alternatives, the scaling step itself, which produces a large set of data-quality indicators, estimation of |F| from intensity and finally examination of intensity statistics to detect crystal pathologies such as twinning. An appendix outlines the scoring schemes used by the program POINTLESS to assign probabilities to possible Laue and space groups.

  3. Atomic Nuclei with Tetrahedral and Octahedral Symmetries

    International Nuclear Information System (INIS)

    Dudek, J.; Gozdz, A.; Schunck, N.

    2003-01-01

    We present possible manifestations of octahedral and tetrahedral symmetries in nuclei. These symmetries are associated with the O D h and T D d double point groups. Both of them have very characteristic finger-prints in terms of the nucleonic level properties - unique in the Fermionic universe. The tetrahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra; it does not preserve the parity. The octahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra as well but it does preserve the parity. Microscopic predictions have been obtained using mean-field theory based on the relativistic equations and confirmed by using ''traditional'' Schrodinger equation formalism. Calculations are performed in multidimensional deformation spaces using newly designed algorithms. We discuss some experimental fingerprints of the hypothetical new symmetries and possibilities of their verification through experiments. (author)

  4. Accidental symmetries and the effective Lagrangian of string theory

    International Nuclear Information System (INIS)

    Ovrut, B.A.

    1989-01-01

    In this paper the relationship between accidental worldsheet symmetries of the string generating functional and target space invariance groups is discussed. Accidental symmetries are used to derive the invariance groups and effective low energy Lagrangian for the bosonic string, and the heterotic string compactified to four-dimensions on Z N orbifolds. The necessity of a new type of Green-Schwarz mechanism, associated with the auxiliary vector field in the four-dimensional N = 1 supergravity multiplet, is shown using these methods

  5. Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

    Science.gov (United States)

    Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang

    2015-01-23

    The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

  6. Symmetries of noncommutative scalar field theory

    International Nuclear Information System (INIS)

    De Goursac, Axel; Wallet, Jean-Christophe

    2011-01-01

    We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit.

  7. Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups

    Science.gov (United States)

    Casas, Lluís; Estop, Euge`nia

    2015-01-01

    Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…

  8. Hidden Symmetries of Stochastic Models

    Directory of Open Access Journals (Sweden)

    Boyka Aneva

    2007-05-01

    Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.

  9. Complete theory of symmetry-based indicators of band topology.

    Science.gov (United States)

    Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

    2017-06-30

    The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

  10. Symmetry and quantum mechanics

    CERN Document Server

    Corry, Scott

    2016-01-01

    This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.

  11. Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

    CERN Document Server

    Hosono, S.; Theisen, S.; Yau, Shing-Tung

    1995-01-01

    We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton corrected Yukawa couplings and the topological one loop partition function to the case of complete intersections with higher dimensional moduli spaces. We will develop a new method of obtaining the instanton corrected Yukawa couplings through a study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the K\\"ahler moduli fields induced from the ambient space for all complete intersections in nonsingular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three generation models which are found in this class. We also apply our method to solve the simplest model in which topology change was observed and discuss examples of complete intersections in singular ambient spaces.

  12. Symmetry-adapted Liouville space. Pt. 8

    International Nuclear Information System (INIS)

    Temme, F.P.

    1990-01-01

    A generalized hierarchy over lexical weight-sets is shown to provide significant insight into the structure of identical higher I i spin clusters under the S n /SO(3) dual groups. The use of combinatorial S n word-lengths allows one to derive the dual irreps directly from the combinatorics inherent in the adapted spin space. These advantages arise from the intimate connections between the scalar invariants of Cayley algebra over a field and their lexical combinatorics over vertical strokeI, Σ i M i , ()> space, which itself is a consequence of the S n -group representational algebra. By taking the highest SO(3) weight as the lexical origin, the calculations become recursive over all further expansions of the spin space, i.e., arising from an enhanced magnitude for the component nuclear spins, I i . The method over Hilbert space for spin clusters of I i ≤ 9/2 is more direct than those associated with unitary group algebras; in addition, the cogent beauty of combinatorial concepts derived from Cayley algebra deserves wider recognition in the physical sciences. (orig.)

  13. Crystal Symmetry Algorithms in a High-Throughput Framework for Materials

    Science.gov (United States)

    Taylor, Richard

    The high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.

  14. Classical symmetries of some two-dimensional models

    International Nuclear Information System (INIS)

    Schwarz, J.H.

    1995-01-01

    It is well-known that principal chiral models and symmetric space models in two-dimensional Minkowski space have an infinite-dimensional algebra of hidden symmetries. Because of the relevance of symmetric space models to duality symmetries in string theory, the hidden symmetries of these models are explored in some detail. The string theory application requires including coupling to gravity, supersymmetrization, and quantum effects. However, as a first step, this paper only considers classical bosonic theories in flat space-time. Even though the algebra of hidden symmetries of principal chiral models is confirmed to include a Kac-Moody algebra (or a current algebra on a circle), it is argued that a better interpretation is provided by a doubled current algebra on a semi-circle (or line segment). Neither the circle nor the semi-circle bears any apparent relationship to the physical space. For symmetric space models the line segment viewpoint is shown to be essential, and special boundary conditions need to be imposed at the ends. The algebra of hidden symmetries also includes Virasoro-like generators. For both principal chiral models and symmetric space models, the hidden symmetry stress tensor is singular at the ends of the line segment. (orig.)

  15. From spin groups and modular P1CT symmetry to covariant representations and the spin-statistics theorem

    International Nuclear Information System (INIS)

    Lorenzen, R.

    2007-03-01

    Starting from the assumption of modular P 1 CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P 1 CT symmetry constitutes no loss of generality because it is a consequence of

  16. Grain size dependent phase stabilities and presence of a monoclinic (Pm) phase in the morphotropic phase boundary region of (1−x)Bi(Mg{sub 1/2}Ti{sub 1/2})O{sub 3}-xPbTiO{sub 3} piezoceramics

    Energy Technology Data Exchange (ETDEWEB)

    Upadhyay, Ashutosh; Singh, Akhilesh Kumar, E-mail: akhilesh-bhu@yahoo.com, E-mail: aksingh.mst@itbhu.ac.in [School of Materials Science and Technology, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005 (India)

    2015-04-14

    Results of the room temperature structural studies on (1−x)Bi(Mg{sub 1/2}Ti{sub 1/2})O{sub 3}-xPbTiO{sub 3} ceramics using Rietveld analysis of the powder x-ray diffraction data in the composition range 0.28 ≤ x ≤ 0.45 are presented. The morphotropic phase boundary region exhibits coexistence of monoclinic (space group Pm) and tetragonal (space group P4 mm) phases in the composition range 0.33 ≤ x ≤ 0.40. The structure is nearly single phase monoclinic (space group Pm) in the composition range 0.28 ≤ x ≤ 0.32. The structure for the compositions with x ≥ 0.45 is found to be predominantly tetragonal with space group P4 mm. Rietveld refinement of the structure rules out the coexistence of rhombohedral and tetragonal phases in the morphotropic phase boundary region reported by earlier authors. The Rietveld structure analysis for the sample x = .35 calcined at various temperatures reveals that phase fraction of the coexisting phases in the morphotropic phase boundary region varies with grain size. The structural parameters of the two coexisting phases also change slightly with changing grain size.

  17. Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

    International Nuclear Information System (INIS)

    Holm, D.D.

    1976-07-01

    The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented

  18. Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

    Energy Technology Data Exchange (ETDEWEB)

    Holm, D.D.

    1976-07-01

    The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.

  19. Symmetry, Symmetry Breaking and Topology

    Directory of Open Access Journals (Sweden)

    Siddhartha Sen

    2010-07-01

    Full Text Available The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.

  20. Crystal structure, equation of state, and elasticity of hydrous aluminosilicate phase, topaz-OH (Al2SiO4(OH)2) at high pressures

    Science.gov (United States)

    Mookherjee, Mainak; Tsuchiya, Jun; Hariharan, Anant

    2016-02-01

    We examined the equation of state and high-pressure elasticity of the hydrous aluminosilicate mineral topaz-OH (Al2SiO4(OH)2) using first principles simulation. Topaz-OH is a hydrous phase in the Al2O3-SiO2-H2O (ASH) ternary system, which is relevant for the mineral phase relations in the hydrated sedimentary layer of subducting slabs. Based on recent neutron diffraction experiments, it is known that the protons in the topaz-OH exhibit positional disorder with half occupancy over two distinct crystallographic sites. In order to adequately depict the proton environment in the topaz-OH, we examined five crystal structure models with distinct configuration for the protons in topaz-OH. Upon full geometry optimization we find two distinct space group, an orthorhombic Pbnm and a monoclinic P21/c for topaz-OH. The topaz-OH with the monoclinic P21/c space group has a lower energy compared to the orthorhombic Pbmn space group symmetry. The pressure-volume results for the monoclinic topaz-OH is well represented by a third order Birch-Murnaghan formulation, with V0mon = 348.63 (±0.04) Å3, K0mon = 164.7 (±0.04) GPa, and K0mon = 4.24 (±0.05). The pressure-volume results for the orthorhombic topaz-OH is well represented by a third order Birch-Murnaghan formulation, with V0orth = 352.47 (±0.04) Å3, K0orth = 166.4 (±0.06) GPa, and K0orth = 4.03 (±0.04). While the bulk moduli are very similar for both the monoclinic and orthorhombic topaz-OH, the shear elastic constants and the shear moduli are very sensitive to the position of the proton, orientation of the O-H dipole, and the space group symmetry. The S-wave anisotropy for the orthorhombic and monoclinic topaz-OH are also quite distinct. In the hydrated sedimentary layer of subducting slabs, transformation of a mineral assemblage consisting of coesite (SiO2) and diaspore (AlOOH) to topaz-OH (Al2SiO4(OH)2) is likely to be accompanied by an increase in density, compressional velocity, and shear wave velocity. However

  1. More on PT-Symmetry in (Generalized Effect Algebras and Partial Groups

    Directory of Open Access Journals (Sweden)

    J. Paseka

    2011-01-01

    Full Text Available We continue in the direction of our paper on PT-Symmetry in (Generalized Effect Algebras and Partial Groups. Namely we extend our considerations to the setting of weakly ordered partial groups. In this setting, any operator weakly ordered partial group is a pasting of its partially ordered commutative subgroups of linear operators with a fixed dense domain over bounded operators. Moreover, applications of our approach for generalized effect algebras are mentioned.

  2. A broken symmetry ontology: Quantum mechanics as a broken symmetry

    International Nuclear Information System (INIS)

    Buschmann, J.E.

    1988-01-01

    The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance

  3. Synthesis of monoclinic potassium niobate nanowires that are stable at room temperature.

    Science.gov (United States)

    Kim, Seungwook; Lee, Ju-Hyuck; Lee, Jaeyeon; Kim, Sang-Woo; Kim, Myung Hwa; Park, Sungnam; Chung, Haegeun; Kim, Yong-Il; Kim, Woong

    2013-01-09

    We report the synthesis of KNbO(3) nanowires (NWs) with a monoclinic phase, a phase not observed in bulk KNbO(3) materials. The monoclinic NWs can be synthesized via a hydrothermal method using metallic Nb as a precursor. The NWs are metastable, and thermal treatment at ∼450 °C changed the monoclinic phase into the orthorhombic phase, which is the most stable phase of KNbO(3) at room temperature. Furthermore, we fabricated energy-harvesting nanogenerators by vertically aligning the NWs on SrTiO(3) substrates. The monoclinic NWs showed significantly better energy conversion characteristics than orthorhombic NWs. Moreover, the frequency-doubling efficiency of the monoclinic NWs was ∼3 times higher than that of orthorhombic NWs. This work may contribute to the synthesis of materials with new crystalline structures and hence improve the properties of the materials for various applications.

  4. Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. II. Minima, symmetries, and topology

    International Nuclear Information System (INIS)

    Ivanov, I. P.

    2008-01-01

    We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of noncontractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/Lagrangian and their spontaneous violation from a wider perspective than usual

  5. El Naschie's Cantorian space-time and general relativity by means of Barbilian's group. A Cantorian fractal axiomatic model of space-time

    International Nuclear Information System (INIS)

    Gottlieb, I.; Agop, M.; Jarcau, M.

    2004-01-01

    One builds the vacuum metrics of the stationary electromagnetic field through the complex potential model. There are thus emphasized both a variational principle, independent on the Ricci tensor, and some internal symmetries of the vacuum solutions. One shows that similar results may be obtained using the Barbiliant's group. By analytical continuation of a Barbilian transformation the link between the fixed points of the modular groups of the vacuum and the golden mean PHI=(1/(1+PHI))=(√5-1)/2 of ε (∞) space-time is established. Finally, a Cantorian fractal axiomatic model of the space-time is presented. The model is explained using a set of coupled equations which may describe the self organizing processes at the solid-liquid, plasma-plasma, and superconductor-superconductor interfaces

  6. Space-charge calculation for bunched beams with 3-D ellipsoidal symmetry

    International Nuclear Information System (INIS)

    Garnett, R.W.; Wangler, T.P.

    1991-01-01

    A method for calculating 3-D space-charge forces has been developed that is suitable for bunched beams of either ions or relativistic electrons. The method is based on the analytic relations between charge-density and electric fields for a distribution with 3-D ellipsoidal symmetry in real space. At each step we use a Fourier-series representation for the smooth particle-density function obtained from the distribution of the macroparticles being tracked through the elements of the system. The resulting smooth electric fields reduce the problem of noise from artificial collisions, associated with small numbers of interacting macroparticles. Example calculations will be shown for comparison with other methods. 4 refs., 2 figs., 1 tab

  7. From spin groups and modular P{sub 1}CT symmetry to covariant representations and the spin-statistics theorem

    Energy Technology Data Exchange (ETDEWEB)

    Lorenzen, R.

    2007-03-15

    Starting from the assumption of modular P{sub 1}CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P{sub 1}CT symmetry constitutes no loss of generality because it is a

  8. Current status and future prospect of space and time reversal symmetry violation on low energy neutron reactions

    International Nuclear Information System (INIS)

    Masuda, Yasuhiro

    1993-01-01

    In this report, the papers on symmetry violation under space reflection and time reversal and neutron spin, neutron spin rotation and P-violation, parity nonconservation in neutron capture reaction, some advantage of the search for CP-violation in neutron scattering, dynamic polarization of 139 La target, alexandrite laser for optical pumping, polarized 3 He system for T- and P-violation neutron experiments, control of neutron spin in T-violation neutron experiment, symmetry regarding time and space and angular distribution and angular correlation of radiation and particle beams, T-violation due to low temperature nuclear polarization and axion exploration using nuclear transition are collected. (K.I.)

  9. The topotactic dehydration of monoclinic {[Co(pht)(bpy)(H2O)2]·2H2O}n into orthorhombic [Co(pht)(bpy)(H2O)2]n (pht is phthalate and bpy is 4,4'-bipyridine).

    Science.gov (United States)

    Harvey, Miguel Angel; Suarez, Sebastián; Cukiernik, Fabio D; Baggio, Ricardo

    2014-10-01

    Controlled heating of single crystals of the previously reported [Köferstein & Robl (2007). Z. Anorg. Allg. Chem. 633, 1127-1130] dihydrate {[Co(pht)(bpy)(H2O)2]·2H2O}n, (II) [where pht is phthalate (C8H4O4) and bpy is 4,4'-bipyridine (C10H8N2)], produced a topotactic transformation into an unreported diaqua anhydrate, namely poly[diaqua(μ2-benzene-1,2-dicarboxylato-κ(2)O(1):O(2))(μ2-4,4'-bipyridine-κ(2)N:N')cobalt(II)], [Co(C8H4O4)(C10H8N2)(H2O)2]n, (IIa). The structural change consists of the loss of the two solvent water molecules linking the original two-dimensional covalent substructures which are the `main frame' of the monoclinic P2/n hydrate (strictly preserved during the transformation), with further reaccommodation of the latter. The anhydrate organizes itself in the orthorhombic system (space group Pmn2(1)) in a disordered fashion, where the space-group-symmetry restrictions are achieved only in a statistical sense, with mirror-related two-dimensional planar substructures, mirrored in a plane perpendicular to [100]. Thus, the asymmetric unit in the refined model is composed of two superimposed mirror-related `ghosts' of half-occupancy each. Similarities and differences with the parent dihydrate and some other related structures in the literature are discussed.

  10. Gauge-Higgs Unification Models in Six Dimensions with S2/Z2 Extra Space and GUT Gauge Symmetry

    Directory of Open Access Journals (Sweden)

    Cheng-Wei Chiang

    2012-01-01

    Full Text Available We review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with S2/Z2 topology in the extra spatial dimensions. Nontrivial boundary conditions are imposed on the extra S2/Z2 space. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12 gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E6 gauge symmetry without requiring the additional symmetry condition. Both models lead to a standard model-like gauge theory with the SU(3×SU(2L×U(1Y(×U(12 symmetry and SM fermions in four dimensions. The Higgs sector of the model is also analyzed. The electroweak symmetry breaking can be realized, and the weak gauge boson and Higgs boson masses are obtained.

  11. Gauging hidden symmetries in two dimensions

    International Nuclear Information System (INIS)

    Samtleben, Henning; Weidner, Martin

    2007-01-01

    We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine e 9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of e 9 . This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of e 9

  12. Symmetry breaking by Wilson loops in gauge field theory

    International Nuclear Information System (INIS)

    Dowker, J.S.; Jadhav, S.P.

    1989-01-01

    An analysis is presented of the gauge symmetry breaking caused by Wilson loops on a space-time whose spatial section is openR/sup d/ x S 3 /Γ, for all those fundamental groups Γ that give a homogeneous space. We concentrate on pure SU(3) and SU(5) gauge field theories and find that symmetry breaking can occur when d = 0, for all Γ. If d = 3, the extra minimal scalars prevent any breaking and one must include other fields to achieve this. Explicit forms for the vacuum energies are exhibited in the case of lens and prism spaces, the former for SU(n). For Γ = Z/sub m/, when m and the radius of the sphere become infinite, we recover the results on the space-time openR/sup d//sup +3/ x S 1

  13. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, Daniel [Ruder Boskovic Institute, Division of Materials Physics, Zagreb (Croatia); Meljanac, Stjepan; Pikutic, Danijel [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia)

    2017-12-15

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)

  14. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    International Nuclear Information System (INIS)

    Meljanac, Daniel; Meljanac, Stjepan; Pikutic, Danijel

    2017-01-01

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)

  15. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    Science.gov (United States)

    Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

    2017-12-01

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

  16. Approximate and renormgroup symmetries

    International Nuclear Information System (INIS)

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  17. Dihedral flavor symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Blum, Alexander Simon

    2009-06-10

    This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D{sub 4}, the other describing quarks and employing the symmetry D{sub 14}. In the latter model it is the quark mixing matrix element V{sub ud} - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations. (orig.)

  18. Dihedral flavor symmetries

    International Nuclear Information System (INIS)

    Blum, Alexander Simon

    2009-01-01

    This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D 4 , the other describing quarks and employing the symmetry D 14 . In the latter model it is the quark mixing matrix element V ud - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations. (orig.)

  19. On the absence of the Efimov effect in spaces of functions of a given symmetry

    International Nuclear Information System (INIS)

    Vugal'ter, S.A.; Zhislin, G.M.

    1981-01-01

    Strict results on the discrete spectrum of Ho three-particle hamiltonians in certain spaces with a Bsup(delta) function of a given symmetry, are formulated. The theorems presented show that in spaces considered with short-acting potentials the Ho . discrete spectrum is finite, i.e. the Efimov effect is impossible. Theorems are proved using the improved techniques on the basis of properties of virtual levels of operators of the energy of the system of two particles in the function spaces [ru

  20. Aqueous-Phase Acetic Acid Ketonization over Monoclinic Zirconia

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Qiuxia [Institute for Integrated Catalysis, Pacific Northwest; College; Lopez-Ruiz, Juan A. [Institute for Integrated Catalysis, Pacific Northwest; Cooper, Alan R. [Institute for Integrated Catalysis, Pacific Northwest; Wang, Jian-guo [College; Albrecht, Karl O. [Institute for Integrated Catalysis, Pacific Northwest; Mei, Donghai [Institute for Integrated Catalysis, Pacific Northwest

    2017-12-13

    The effect of aqueous phase on the acetic acid ketonization over monoclinic zirconia has been investigated using first-principles based density functional theory (DFT) calculations. To capture the aqueous phase chemistry over the solid zirconia catalyst surface, the aqueous phase is represented by 111 explicit water molecules with a liquid water density of 0.93 g/cm3 and the monoclinic zirconia is modeled by the most stable surface structure . The dynamic nature of aqueous phase/ interface was studied using ab initio molecular dynamics simulation, indicating that nearly half of the surface Zr sites are occupied by either adsorbed water molecules or hydroxyl groups at 550 K. DFT calculations show that the adsorption process of acetic acid from the liquid water phase to the surface is nearly thermodynamically neutral with a Gibbs free energy of -2.3 kJ/mol although the adsorption strength of acetic acid on the surface in aqueous phase is much stronger than in vapor phase. Therefore it is expected that the adsorption of acetic acid will dramatically affects aqueous phase ketonization reactivity over the monoclinic zirconia catalyst. Using the same ketonization mechanism via the β-keto acid intermediate, we have compared acetic acid ketonization to acetone in both vapor and aqueous phases. Our DFT calculation results show although the rate-determining step of the β-keto acid formation via the C-C coupling is not pronouncedly affected, the presence of liquid water molecules will dramatically affect dehydrogenation and hydrogenation steps via proton transfer mechanism. This work was financially supported by the United States Department of Energy (DOE)’s Bioenergy Technologies Office (BETO) and performed at the Pacific Northwest National Laboratory (PNNL). PNNL is a multi-program national laboratory operated for DOE by Battelle Memorial Institute. Computing time and advanced catalyst characterization use was granted by a user proposal at the William R. Wiley

  1. Approximate and renormgroup symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  2. Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors

    Directory of Open Access Journals (Sweden)

    Andrei A. Malykh

    2013-11-01

    Full Text Available We demonstrate how a combination of our recently developed methods of partner symmetries, symmetry reduction in group parameters and a new version of the group foliation method can produce noninvariant solutions of complex Monge-Ampère equation (CMA and provide a lift from invariant solutions of CMA satisfying Boyer-Finley equation to non-invariant ones. Applying these methods, we obtain a new noninvariant solution of CMA and the corresponding Ricci-flat anti-self-dual Einstein-Kähler metric with Euclidean signature without Killing vectors, together with Riemannian curvature two-forms. There are no singularities of the metric and curvature in a bounded domain if we avoid very special choices of arbitrary functions of a single variable in our solution. This metric does not describe gravitational instantons because the curvature is not concentrated in a bounded domain.

  3. Quasi Hopf quantum symmetry in quantum theory

    International Nuclear Information System (INIS)

    Mack, G.; Schomerus, V.

    1991-05-01

    In quantum theory, internal symmetries more general than groups are possible. We show that quasitriangular quasi Hopf algebras G * as introduced by Drinfeld permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators as proposed by Froehlich. All this remains true when Drinfelds axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasitriangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G * admits a * -operation with certain properties. Invariance properties of Greens functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like U q (sl 2 ) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasitriangular quasi Hopf algebra G * is canonically associated with U q (sl 2 ) if q P =-1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)

  4. The extensions of space-time. Physics in the 8-dimensional homogeneous space D = SU(2,2)/K

    International Nuclear Information System (INIS)

    Barut, A.O.

    1993-07-01

    The Minkowski space-time is only a boundary of a bigger homogeneous space of the conformal group. The conformal group is the symmetry group of our most fundamental massless wave equations. These extended groups and spaces have many remarkable properties and physical implications. (author). 36 refs

  5. Generating Lie Point Symmetry Groups of (2+1)-Dimensional Broer-Kaup Equation via a Simple Direct Method

    International Nuclear Information System (INIS)

    Ma Hongcai

    2005-01-01

    Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.

  6. Weak C* Hopf Symmetry

    OpenAIRE

    Rehren, K. -H.

    1996-01-01

    Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.

  7. Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.

    Science.gov (United States)

    Nascimento, Daniel R; DePrince, A Eugene

    2018-05-08

    The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ 2 and Ŝ 3 ) symmetry breaking properties. When imposing Ŝ 2 and Ŝ 3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H 2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ 2 and Ŝ 3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.

  8. The representation theory of the symmetry group of lattice fermions as a basis for kinematics in lattice QCD

    International Nuclear Information System (INIS)

    Joos, H.; Schaefer, M.

    1987-01-01

    The symmetry group of staggered lattice fermions is discussed as a discrete subgroup of the symmetry group of the Dirac-Kaehler equation. For the representation theory of this group, G. Mackey's generalization of E.P. Wigner's procedure for the construction of unitary representations of groups with normal subgroups is used. A complete classification of these irreducible representations by ''momentum stars'', ''flavour orbits'' and ''reduced spins'' is given. (orig.)

  9. Ab initio velocity-field curves in monoclinic β-Ga2O3

    Science.gov (United States)

    Ghosh, Krishnendu; Singisetti, Uttam

    2017-07-01

    We investigate the high-field transport in monoclinic β-Ga2O3 using a combination of ab initio calculations and full band Monte Carlo (FBMC) simulation. Scattering rate calculation and the final state selection in the FBMC simulation use complete wave-vector (both electron and phonon) and crystal direction dependent electron phonon interaction (EPI) elements. We propose and implement a semi-coarse version of the Wannier-Fourier interpolation method [Giustino et al., Phys. Rev. B 76, 165108 (2007)] for short-range non-polar optical phonon (EPI) elements in order to ease the computational requirement in FBMC simulation. During the interpolation of the EPI, the inverse Fourier sum over the real-space electronic grids is done on a coarse mesh while the unitary rotations are done on a fine mesh. This paper reports the high field transport in monoclinic β-Ga2O3 with deep insight into the contribution of electron-phonon interactions and velocity-field characteristics for electric fields ranging up to 450 kV/cm in different crystal directions. A peak velocity of 2 × 107 cm/s is estimated at an electric field of 200 kV/cm.

  10. Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in between

    Directory of Open Access Journals (Sweden)

    Alexis De Vos

    2011-06-01

    Full Text Available Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qubit, the transformation being controlled by the other w−1 (qubits. We explain why the former circuit can be decomposed into 2w − 1 control gates, whereas the latter circuit needs 2w − 1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w − 1 or into 2w − 1 control gates.

  11. Spinor Structure and Internal Symmetries

    Science.gov (United States)

    Varlamov, V. V.

    2015-10-01

    Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.

  12. Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

    Directory of Open Access Journals (Sweden)

    Oleg I. Morozov

    2005-10-01

    Full Text Available In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equation and the Euler-Poisson equation.

  13. Geometry, rigidity, and group actions

    CERN Document Server

    Farb, Benson; Zimmer, Robert J

    2011-01-01

    The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others.The p

  14. Generalized global symmetries

    International Nuclear Information System (INIS)

    Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; Willett, Brian

    2015-01-01

    A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

  15. Ceramic fiber-reinforced monoclinic celsian phase glass-ceramic matrix composite material

    Science.gov (United States)

    Bansal, Narottam P. (Inventor); Dicarlo, James A. (Inventor)

    1994-01-01

    A hyridopolysilazane-derived ceramic fiber reinforced monoclinic celsian phase barium aluminum silicate glass-ceramic matrix composite material is prepared by ball-milling an aqueous slurry of BAS glass powder and fine monoclinic celsian seeds. The fibers improve the mechanical strength and fracture toughness and with the matrix provide superior dielectric properties.

  16. On the structure of physical space

    CERN Document Server

    Wisnivesky, D

    2001-01-01

    In this paper we develop a theory based on the postulate that the environment where physical phenomena take place is the space of four complex parameters of the linear group of transformations. Using these parameters as fundamental building blocks we construct ordinary space-time and the internal space. Lorentz invariance is built in the definition of external space, while the symmetry of the internal space, S(1)*SU(2) results as a consequence of the identification of the external coordinates. Thus, special relativity and the electroweak interaction symmetry ensue from the properties of the basic building blocks of physical space. Since internal and external space are derived from a common structure, there is no need to bring into the theory any additional hypothesis to account for the microscopic nature of the internal space, nor to introduce symmetry breaking mechanisms that would normally be required to force a splitting of the internal and external symmetries. As an outcome of the existence of a basic str...

  17. Localizability and local gauge symmetry in quantum theory

    International Nuclear Information System (INIS)

    Leveille, J.P.

    1976-01-01

    An attempt is made to generalize a theorem of Jauch on the equivalence of local gauge symmetry and Galilean symmetry to relativistic theories. One first proves a converse to Jauch's theorem deriving the Galilei algebra from a locality postulate. When generalized to the relativistic case the locality postulate leads one to the relativistic dynamical group g 5 . A possible physical interpretation of g 5 as a relativistic dynamical group is given. An attempt to describe the dynamics solely in Minkowski space-time leads, in conjunction with the locality postulate, to a new relativistic dynamical algebra. We found that this new algebra is realized by field theoretical examples which exclude quantum electrodynamics, however, and other known gauge theories. This latter development forces one to seriously question the validity of the locality postulate. One concludes by proving a general theorem about the nonimplementability of local transformations by global operators independent of space-time in field theory

  18. The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons

    International Nuclear Information System (INIS)

    El Naschie, M.S.

    2008-01-01

    New insights into the structure of various exceptional Lie symmetry groups hierarchies are utilized to shed light on various problems pertinent to the standard model of high energy physics and the Higgs

  19. New symmetries for the gravitational S-matrix

    International Nuclear Information System (INIS)

    Campiglia, Miguel; Laddha, Alok

    2015-01-01

    In http://dx.doi.org/10.1103/PhysRevD.90.124028 we proposed a generalization of the BMS group G which is a semi-direct product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S 2 ) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S 2 ) charges which we could not derive from first principles as G does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S 2 ) charges. The result of this paper, in conjunction with the results of http://arxiv.org/abs/1401.7026http://dx.doi.org/10.1103/PhysRevD.90.124028 prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to G.

  20. Twistor space, Minkowski space and the conformal group

    International Nuclear Information System (INIS)

    Broek, P.M. van den

    1983-01-01

    It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the transformation of twistor space under space inversion and time inversion. (orig.)

  1. Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system

    International Nuclear Information System (INIS)

    Cherniha, Roman; Davydovych, Vasyl’

    2013-01-01

    Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)

  2. 8x8 and 10x10 Hyperspace Representations of SU(3) and 10-fold Point-Symmetry Group of Quasicrystals

    Science.gov (United States)

    Animalu, Alexander

    2012-02-01

    In order to further elucidate the unexpected 10-fold point-symmetry group structure of quasi-crystals for which the 2011 Nobel Prize in chemistry was awarded to Daniel Shechtman, we explore a correspondence principle between the number of (projective) geometric elements (points[vertices] + lines[edges] + planes[faces]) of primitive cells of periodic or quasi-periodic arrangement of hard or deformable spheres in 3-dimensional space of crystallography and elements of quantum field theory of particle physics [points ( particles, lines ( particles, planes ( currents] and hence construct 8x8 =64 = 28+36 = 26 + 38, and 10x10 =100= 64 + 36 = 74 + 26 hyperspace representations of the SU(3) symmetry of elementary particle physics and quasicrystals of condensed matter (solid state) physics respectively, As a result, we predict the Cabibbo-like angles in leptonic decay of hadrons in elementary-particle physics and the observed 10-fold symmetric diffraction pattern of quasi-crystals.

  3. Is CP a gauge symmetry?

    International Nuclear Information System (INIS)

    Choi, K.; Kaplan, D.B.; Nelson, A.E.

    1993-01-01

    Conventional solutions to the strong CP problem all require the existence of global symmetries. However, quantum gravity may destroy global symmetries, making it hard to understand why the electric dipole moment of the neutron (EDMN) is so small. We suggest here that CP is actually a discrete gauge symmetry, and is therefore not violated by quantum gravity. We show that four-dimensional CP can arise as a discrete gauge symmetry in theories with dimensional compactification, if the original number of Minkowski dimensions equals 8k+1, 8k+2 or 8k+3, and if there are certain restrictions on the gauge group; these conditions are met by superstrings. CP may then be broken spontaneously below 10 9 GeV, explaining the observed CP violation in the kaon system without inducing a large EDMN. We discuss the phenomenology of such models, as well as the peculiar properties of cosmic 'SP strings' which could be produced at the compactification scale. Such strings have the curious property that a particle carried around the string is turned into its CP conjugate. A single CP string renders four-dimensional space-time nonorientable. (orig.)

  4. The renormalization group of relativistic quantum field theory as a set of generalized, spontaneously broken, symmetry transformations

    International Nuclear Information System (INIS)

    Maris, Th.A.J.

    1976-01-01

    The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt

  5. Characterization of a Diamond Ground Y-TZP and Reversion of the Tetragonal to Monoclinic Transformation.

    Science.gov (United States)

    Candido, L M; Fais, Lmg; Ferreira, E B; Antonio, S G; Pinelli, Lap

    To characterize the surface of an yttria-stabilized zirconia (Y-TZP) ceramic after diamond grinding in terms of its crystalline phase, morphology, mean roughness (Ra), and wettability as well as to determine a thermal treatment to reverse the resulting tetragonal to monoclinic (t-m) transformation. Y-TZP specimens were distributed into different groups according to the actions (or no action) of grinding and irrigation. Grinding was accomplished using a diamond stone at a low speed. The samples were characterized by x-ray diffraction (XRD), scanning electron microscopy, goniometry, and profilometry. In situ high-temperature XRD was used to determine an annealing temperature to reverse the t-m transformation. Ra was submitted to the Kruskal-Wallis test, followed by the Dunn test (α=0.05). The volume fraction of the monoclinic phase and contact angle were submitted to one-way analysis of variance, followed by the Tukey test (α=0.05). Monoclinic zirconia was observed on the surface of samples after dry and wet grinding with a diamond stone. The volume fraction of the monoclinic phase was smaller on the dry ground samples (3.6%±0.3%) than on the wet ground samples (5.6%±0.3%). High-temperature XRD showed reversion of the t-m phase transformation, which started at 700°C and completed at 800°C in a conventional oven. Grinding with a diamond stone partially transformed the crystalline phase on the surface of a Y-TZP ceramic from tetragonal to monoclinic zirconia while simultaneously increasing the surface roughness and wettability. The t-m transformation could be reversed by heat treatment at 800°C or 900°C for 60 minutes or 1000°C for 30 minutes.

  6. Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

    Directory of Open Access Journals (Sweden)

    Christian Appold

    2010-06-01

    Full Text Available One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking.

  7. New Insights into Viral Architecture via Affine Extended Symmetry Groups

    Directory of Open Access Journals (Sweden)

    T. Keef

    2008-01-01

    Full Text Available Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognized that icosahedral symmetry is crucial for the structural organization of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, a prediction on the relative sizes of different virus particles in a family cannot be made. Moreover, information on the full 3D structure of viral particles, including the tertiary structures of the capsid proteins and the organization of the viral genome within the capsid are inaccessible with their approach. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to address these issues. In particular, we show that the relative radii of viruses in the family of Polyomaviridae and the material boundaries in simple RNA viruses can be determined with our approach. The results complement Caspar and Klug's theory of quasi-equivalence and provide details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.

  8. Supergauge symmetry in local quantum field theory

    International Nuclear Information System (INIS)

    Ferrara, S.

    1974-01-01

    The extension of supergauge symmetry to four-dimensional space-time allows to investigate the possible role of this symmetry in conventional local quantum field theory. The supergauge algebra is obtained by adding to the conformal group of space-time two Majorana spinor generators and the chiral charge. The commutation properties of the algebra are used to derive the most general form of the superfield. This field contains two Majorana spinors, two scalar fields, a chiral doublet, and a real vector field called the vector superfield. The covariant derivatives defined, together with the scalar and vector multiplets are the basic ingredients used in order to build up supergauge symmetric Lagrangians. It is shown that the only possible fields which can be considered as supergauge invariant Lagrangians are the F and D components of the scalar and vector multiplets respectively

  9. Ricci inheritance symmetry in general relativity

    International Nuclear Information System (INIS)

    Bokhari, A.H.; Al-Dweik, A.; Zaman, F.D.; Karim, M.; Kubel, D.

    2010-01-01

    In an earlier paper (see Nuovo Cimento B, 19 (2004) 1187) it was conjectured that none of the well-known spherically symmetric static space-time solutions of the Einstein equations admit non-trivial Ricci inheritance symmetry. In this paper we discuss Ricci inheritance (R I) symmetry in three well-known non static spherically symmetric space-time metrics and show that our conjecture is also valid in non-static space-time metrics.

  10. Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

    NARCIS (Netherlands)

    de Klerk, E.; Sotirov, R.

    2007-01-01

    We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,

  11. Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

    Science.gov (United States)

    Zhou, L.-Q.; Meleshko, S. V.

    2017-07-01

    The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

  12. Lie symmetries for systems of evolution equations

    Science.gov (United States)

    Paliathanasis, Andronikos; Tsamparlis, Michael

    2018-01-01

    The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

  13. Magnetic superspace groups and symmetry constraints in incommensurate magnetic phases

    International Nuclear Information System (INIS)

    Perez-Mato, J M; Aroyo, M I; Ribeiro, J L; Petricek, V

    2012-01-01

    Superspace symmetry has been for many years the standard approach for the analysis of non-magnetic modulated crystals because of its robust and efficient treatment of the structural constraints present in incommensurate phases. For incommensurate magnetic phases, this generalized symmetry formalism can play a similar role. In this context we review from a practical viewpoint the superspace formalism particularized to magnetic incommensurate phases. We analyse in detail the relation between the description using superspace symmetry and the representation method. Important general rules on the symmetry of magnetic incommensurate modulations with a single propagation vector are derived. The power and efficiency of the method is illustrated with various examples, including some multiferroic materials. We show that the concept of superspace symmetry provides a simple, efficient and systematic way to characterize the symmetry and rationalize the structural and physical properties of incommensurate magnetic materials. This is especially relevant when the properties of incommensurate multiferroics are investigated. (topical review)

  14. A monoclinic polymorph of theophylline

    Directory of Open Access Journals (Sweden)

    Shuo Zhang

    2011-12-01

    Full Text Available A monoclinic polymorph of theophylline, C7H8N4O2, has been obtained from a chloroform/methanol mixture by evaporation under ambient conditions. The new polymorph crystallizes with two molecules in the asymmetric unit. The structure features intermolecular N—H...O hydrogen bonds, resulting in the formation of dimers between two crystallographically different molecules; each molecule acts as both donor and acceptor.

  15. The effect of crystal symmetry on the maximum polarization of polycrystalline ferroelectric materials

    International Nuclear Information System (INIS)

    Jones, Jacob L.

    2010-01-01

    In polycrystalline ceramics, the degree of domain orientation in all possible crystal orientations contributes to the total realizable polarization. The extent to which domains are oriented towards an applied field can be described by a polarization distribution function. Such representations are calculated and presented in the present work for several different crystal systems including monoclinic symmetries that exhibit a polarization rotation mechanism. The relationship between the polarization distribution functions and the attainable macroscopic polarization is also developed for polycrystalline ceramics that are initially randomly oriented. In these cases, polarization rotation allows a significant degree of preferred orientation parallel to the electric field (>1000 multiples of a random distribution). However, the fraction of single crystal polarization that can be achieved (97.5%) is only marginally better than those of higher crystal symmetry.

  16. Emergent Low-Symmetry Phases and Large Property Enhancements in Ferroelectric KNbO 3 Bulk Crystals

    Energy Technology Data Exchange (ETDEWEB)

    Lummen, Tom T. A. [Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 USA; Leung, J. [Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 USA; Kumar, Amit [School of Mathematics and Physics, Queen' s University Belfast, University Road, Belfast BT71NN Northern Ireland UK; Wu, X. [Department of Physics, University of Texas at Austin, Austin TX 78712 USA; Ren, Y. [Department of Physics, University of Texas at Austin, Austin TX 78712 USA; VanLeeuwen, Brian K. [Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 USA; Haislmaier, Ryan C. [Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 USA; Holt, Martin [Center for Nanoscale Materials, Argonne National Laboratory, Argonne IL 60439 USA; Lai, Keji [Department of Physics, University of Texas at Austin, Austin TX 78712 USA; Kalinin, Sergei V. [Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge TN 37831 USA; Gopalan, Venkatraman [Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802 USA

    2017-06-19

    The design of new or enhanced functionality in materials is traditionally viewed as requiring the discovery of new chemical compositions through synthesis. Large property enhancements may however also be hidden within already well-known materials, when their structural symmetry is deviated from equilibrium through a small local strain or field. Here, the discovery of enhanced material properties associated with a new metastable phase of monoclinic symmetry within bulk KNbO3 is reported. This phase is found to coexist with the nominal orthorhombic phase at room temperature, and is both induced by and stabilized with local strains generated by a network of ferroelectric domain walls. While the local microstructural shear strain involved is only approximate to 0.017%, the concurrent symmetry reduction results in an optical second harmonic generation response that is over 550% higher at room temperature. Moreover, the meandering walls of the low-symmetry domains also exhibit enhanced electrical conductivity on the order of 1 S m(-1). This discovery reveals a potential new route to local engineering of significant property enhancements and conductivity through symmetry lowering in ferroelectric crystals.

  17. Crystal-field energy level analysis for Nd3+ ions at the low symmetry C1 site in [Nd(hfa)4(H2O)](N(C2H5)4) single crystals

    International Nuclear Information System (INIS)

    Mech, Agnieszka; Gajek, Zbigniew; Karbowiak, Miroslaw; Rudowicz, Czeslaw

    2008-01-01

    Optical absorption measurements of Nd 3+ ions in single crystals of [Nd(hfa) 4 (H 2 O)](N(C 2 H 5 ) 4 ) (hfa = hexafluoroacetyloacetonate), denoted Nd(hfa) for short, have been carried out at 4.2 and 298 K. This compound crystallizes in the monoclinic system (space group P 2 1 /n). Each Nd ion is coordinated to eight oxygen atoms that originate from the hexafluoroacetylacetonate ligands and one oxygen atom from the water molecule. A total of 85 experimental crystal-field (CF) energy levels arising from the Nd 3+ (4f 3 ) electronic configuration were identified in the optical spectra and assigned. A three-step CF analysis was carried out in terms of a parametric Hamiltonian for the actual C 1 symmetry at the Nd 3+ ion sites. In the first step, a total of 27 CF parameters (CFPs) in the Wybourne notation B kq , admissible by group theory, were determined in a preliminary fitting constrained by the angular overlap model predictions. The resulting CFP set was reduced to 24 specific independent CFPs using appropriate standardization transformations. Optimizations of the second-rank CFPs and extended scanning of the parameter space were employed in the second step to improve reliability of the CFP sets, which is rather a difficult task in the case of no site symmetry. Finally, seven free-ion parameters and 24 CFPs were freely varied, yielding an rms deviation between the calculated energy levels and the 85 observed ones of 11.1 cm -1 . Our approach also allows prediction of the energy levels of Nd 3+ ions that are hidden in the spectral range overlapping with strong ligand absorption, which is essential for understanding the inter-ionic energy transfer. The orientation of the axis system associated with the fitted CF parameters w.r.t. the crystallographic axes is established. The procedure adopted in our calculations may be considered as a general framework for analysis of CF levels of lanthanide ions at low (triclinic) symmetry sites

  18. Crystal-field energy level analysis for Nd(3+) ions at the low symmetry C(1) site in [Nd(hfa)(4)(H(2)O)](N(C(2)H(5))(4)) single crystals.

    Science.gov (United States)

    Mech, Agnieszka; Gajek, Zbigniew; Karbowiak, Mirosław; Rudowicz, Czesław

    2008-09-24

    Optical absorption measurements of Nd(3+) ions in single crystals of [Nd(hfa)(4)(H(2)O)](N(C(2)H(5))(4)) (hfa = hexafluoroacetyloacetonate), denoted Nd(hfa) for short, have been carried out at 4.2 and 298 K. This compound crystallizes in the monoclinic system (space group P 2(1)/n). Each Nd ion is coordinated to eight oxygen atoms that originate from the hexafluoroacetylacetonate ligands and one oxygen atom from the water molecule. A total of 85 experimental crystal-field (CF) energy levels arising from the Nd(3+) (4f(3)) electronic configuration were identified in the optical spectra and assigned. A three-step CF analysis was carried out in terms of a parametric Hamiltonian for the actual C(1) symmetry at the Nd(3+) ion sites. In the first step, a total of 27 CF parameters (CFPs) in the Wybourne notation B(kq), admissible by group theory, were determined in a preliminary fitting constrained by the angular overlap model predictions. The resulting CFP set was reduced to 24 specific independent CFPs using appropriate standardization transformations. Optimizations of the second-rank CFPs and extended scanning of the parameter space were employed in the second step to improve reliability of the CFP sets, which is rather a difficult task in the case of no site symmetry. Finally, seven free-ion parameters and 24 CFPs were freely varied, yielding an rms deviation between the calculated energy levels and the 85 observed ones of 11.1 cm(-1). Our approach also allows prediction of the energy levels of Nd(3+) ions that are hidden in the spectral range overlapping with strong ligand absorption, which is essential for understanding the inter-ionic energy transfer. The orientation of the axis system associated with the fitted CF parameters w.r.t. the crystallographic axes is established. The procedure adopted in our calculations may be considered as a general framework for analysis of CF levels of lanthanide ions at low (triclinic) symmetry sites.

  19. Crystal-field energy level analysis for Nd3+ ions at the low symmetry C1 site in [Nd(hfa)4(H2O)](N(C2H5)4) single crystals

    Science.gov (United States)

    Mech, Agnieszka; Gajek, Zbigniew; Karbowiak, Mirosław; Rudowicz, Czesław

    2008-09-01

    Optical absorption measurements of Nd3+ ions in single crystals of [Nd(hfa)4(H2O)](N(C2H5)4) (hfa = hexafluoroacetyloacetonate), denoted Nd(hfa) for short, have been carried out at 4.2 and 298 K. This compound crystallizes in the monoclinic system (space group P 21/n). Each Nd ion is coordinated to eight oxygen atoms that originate from the hexafluoroacetylacetonate ligands and one oxygen atom from the water molecule. A total of 85 experimental crystal-field (CF) energy levels arising from the Nd3+ (4f3) electronic configuration were identified in the optical spectra and assigned. A three-step CF analysis was carried out in terms of a parametric Hamiltonian for the actual C1 symmetry at the Nd3+ ion sites. In the first step, a total of 27 CF parameters (CFPs) in the Wybourne notation Bkq, admissible by group theory, were determined in a preliminary fitting constrained by the angular overlap model predictions. The resulting CFP set was reduced to 24 specific independent CFPs using appropriate standardization transformations. Optimizations of the second-rank CFPs and extended scanning of the parameter space were employed in the second step to improve reliability of the CFP sets, which is rather a difficult task in the case of no site symmetry. Finally, seven free-ion parameters and 24 CFPs were freely varied, yielding an rms deviation between the calculated energy levels and the 85 observed ones of 11.1 cm-1. Our approach also allows prediction of the energy levels of Nd3+ ions that are hidden in the spectral range overlapping with strong ligand absorption, which is essential for understanding the inter-ionic energy transfer. The orientation of the axis system associated with the fitted CF parameters w.r.t. the crystallographic axes is established. The procedure adopted in our calculations may be considered as a general framework for analysis of CF levels of lanthanide ions at low (triclinic) symmetry sites.

  20. Quasi-Rayleigh waves in transversely isotropic half-space with inclined axis of symmetry

    International Nuclear Information System (INIS)

    Yanovskaya, T.B.; Savina, L.S.

    2003-09-01

    A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in the case of Rayleigh wave in isotropic half-space. Though the theory is simple enough, a numerical procedure for the calculation of surface wave velocity presents some difficulties. The difficulty is conditioned by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of nonlinear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in isotropic half-space. Unlike Rayleigh wave in isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincide with the direction of propagation only in azimuths 0 deg. (180 deg.) and 90 deg. (270 deg.). (author)

  1. Theory of color symmetry for periodic and quasiperiodic crystals

    International Nuclear Information System (INIS)

    Lifshitz, R.

    1997-01-01

    The author presents a theory of color symmetry applicable to the description and classification of periodic as well as quasiperiodic colored crystals. This theory is an extension to multicomponent fields of the Fourier-space approach of Rokhsar, Wright, and Mermin. It is based on the notion of indistinguishability and a generalization of the traditional concepts of color point group and color space group. The theory is applied toward (I) the classification of all black and white space-group types on standard axial quasicrystals in two and three dimensions; (II) the classification of all black and white space-group types in the icosahedral system; (III) the determination of the possible numbers of colors in a standard two-dimensional N-fold symmetric color field whose components are all indistinguishable; and (IV) the classification of two-dimensional decagonal and pentagonal n-color space-group types, explicitly listed for n≤25. copyright 1997 The American Physical Society

  2. Simple mathematical models of symmetry breaking. Application to particle physics

    International Nuclear Information System (INIS)

    Michel, L.

    1976-01-01

    Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)

  3. From groups to geometry and back

    CERN Document Server

    Climenhaga, Vaughn

    2017-01-01

    Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering space...

  4. Lifting the geometric frustration through a monoclinic distortion in “114” YBaFe4O7.0: Magnetism and transport

    International Nuclear Information System (INIS)

    Duffort, V.; Sarkar, T.; Caignaert, V.; Pralong, V.; Raveau, B.; Avdeev, M.; Cervellino, A.; Waerenborgh, J.C.; Tsipis, E.V.

    2013-01-01

    The possibility to lift the geometric frustration in the “114” stoichiomeric tetragonal oxide YBaFe 4 O 7.0 by decreasing the temperature has been investigated using neutron and synchrotron powder diffraction techniques. Besides the structural transition from tetragonal to monoclinic symmetry that appears at T S =180 K, a magnetic transition is observed below T N =95 K. The latter corresponds to a lifting of the 3D geometric frustration toward an antiferromagnetic long range ordering, never observed to date in a cubic based “114’” oxide. The magnetic structure, characterized by the propagation vector k 1 =(0,0,½), shows that one iron Fe2 exhibits a larger magnetic moment than the three others, suggesting a possible charge ordering according to the formula YBaFe 3+ Fe 3 2+ O 7.0 . The magnetic M(T) and χ′(T) curves, in agreement with neutron data, confirm the structural and magnetic transitions and evidence the coexistence of residual magnetic frustration. Moreover, the transport measurements show a resistive transition from a thermally activated conduction mechanism to a variable range hopping mechanism at T S =180 K, with a significant increase of the dependence of the resistivity vs. temperature. Mössbauer spectroscopy clearly evidences a change in the electronic configuration of the iron framework at the structural transition as well as coexistence of several oxidation states. The role of barium underbonding in these transitions is discussed. - Graphical abstract: Atomic displacements at the tetragonal-monoclinic transition in YBaFe 4 O 7 . Display Omitted - Highlights: • The structural and magnetic phase transitions of YBaFe 4 O 7 were studied below room temperature. • The tetragonal to monoclinic transition, characterized by NPD and SXRD, was studied using mode crystallography approach. • Monoclinic distortion allows the lifting of the geometrical frustration on the iron sublattice, leading to AF order at T=95 K

  5. Twistor space, Minkowski space and the conformal group

    NARCIS (Netherlands)

    van den Broek, P.M.

    1983-01-01

    It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the

  6. Infinite-Order Symmetries for Quantum Separable Systems

    International Nuclear Information System (INIS)

    Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.

    2005-01-01

    We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, we can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries

  7. Infinite-order symmetries for quantum separable systems

    International Nuclear Information System (INIS)

    Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.

    2005-01-01

    A calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space is developed. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, it can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries [ru

  8. Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    Defenu, N.; Mati, P.; Márián, I.G.; Nándori, I.; Trombettoni, A.

    2015-01-01

    We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N=1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.

  9. Killing symmetries in neutron transport

    International Nuclear Information System (INIS)

    Lukacs, B.; Racz, A.

    1992-10-01

    Although inside the reactor zone there is no exact continuous spatial symmetry, in certain configurations neutron flux distribution is close to a symmetrical one. In such cases the symmetrical solution could provide a good starting point to determine the non-symmetrical power distribution. All possible symmetries are determined in the 3-dimensional Euclidean space, and the form of the transport equation is discussed in such a coordinate system which is adapted to the particular symmetry. Possible spontaneous symmetry breakings are pointed out. (author) 6 refs

  10. On systems having Poincaré and Galileo symmetry

    International Nuclear Information System (INIS)

    Holland, Peter

    2014-01-01

    Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics

  11. Spatially-protected Topology and Group Cohomology in Band Insulators

    Science.gov (United States)

    Alexandradinata, A.

    This thesis investigates band topologies which rely fundamentally on spatial symmetries. A basic geometric property that distinguishes spatial symmetry regards their transformation of the spatial origin. Point groups consist of spatial transformations that preserve the spatial origin, while un-split extensions of the point groups by spatial translations are referred to as nonsymmorphic space groups. The first part of the thesis addresses topological phases with discretely-robust surface properties: we introduce theories for the Cnv point groups, as well as certain nonsymmorphic groups that involve glide reflections. These band insulators admit a powerful characterization through the geometry of quasimomentum space; parallel transport in this space is represented by the Wilson loop. The non-symmorphic topology we study is naturally described by a further extension of the nonsymmorphic space group by quasimomentum translations (the Wilson loop), thus placing real and quasimomentum space on equal footing -- here, we introduce the language of group cohomology into the theory of band insulators. The second part of the thesis addresses topological phases without surface properties -- their only known physical consequences are discrete signatures in parallel transport. We provide two such case studies with spatial-inversion and discrete-rotational symmetries respectively. One lesson learned here regards the choice of parameter loops in which we carry out transport -- the loop must be chosen to exploit the symmetry that protects the topology. While straight loops are popular for their connection with the geometric theory of polarization, we show that bent loops also have utility in topological band theory.

  12. Laughlin states on the Poincare half-plane and its quantum group symmetry

    OpenAIRE

    Alimohammadi, M.; Sadjadi, H. Mohseni

    1996-01-01

    We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.

  13. Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

    CERN Document Server

    Berglund, P; Klemm, A D

    1995-01-01

    The moduli dependence of (2,2) superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg orbifolds with c=9 whose potential is a sum of A-type singularities. Here we consider the generalization to arbitrary quasi-homogeneous singularities at c=9. We use mirror symmetry to derive the dependence of the models on the complexified K\\"ahler moduli and check the expansions of some topological correlation functions against explicit genus zero and genus one instanton calculations. As an important application we give examples of how non-algebraic (``twisted'') deformations can be mapped to algebraic ones, hence allowing us to study the full moduli space. We also study how moduli spaces can be nested in each other, thus enabling a (singular) transition from one theory to another. Following the recent work of Greene, Morrison and Strominger we show that this corresponds to bla...

  14. Integrating Symmetry in Stereochemical Analysis in Introductory Organic Chemistry

    Science.gov (United States)

    Taagepera, Mare; Arasasingham, Ramesh D.; King, Susan; Potter, Frank; Martorell, Ingrid; Ford, David; Wu, Jason; Kearney, Aaron M.

    2011-01-01

    We report a comparative study using "knowledge space theory" (KAT) to assess the impact of a hands-on laboratory exercise that used molecular model kits to emphasize the connections between a plane of symmetry, Charity, and isomerism in an introductory organic chemistry course. The experimental design compared three groups of…

  15. Quantum group and symmetry of the heat equation

    International Nuclear Information System (INIS)

    Jha, P.K.; Tripathy, K.C.

    1992-07-01

    The symmetry associated with the heat equation is re-examined using Lie's method. Under suitable choice of the arbitrary parameters in the Lie field, it is shown that the system exhibits SL(2,R) symmetry. On inspection of the q-analogue of the principal solution, we find broadening of the Gaussian-flow curve when q is varied from 1 to 0.002. The q-analogue of the general solution predicts the existence of additional degeneracy. (author). 8 refs, 1 fig

  16. Symmetry-adapted configurational modelling of fractional site occupancy in solids

    Energy Technology Data Exchange (ETDEWEB)

    Grau-Crespo, R [Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); Hamad, S [Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); Catlow, C R A [Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); Leeuw, N H de [Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom)

    2007-06-27

    A methodology is presented, which reduces the number of site-occupancy configurations to be calculated when modelling site disorder in solids, by taking advantage of the crystal symmetry of the lattice. Within this approach, two configurations are considered equivalent when they are related by an isometric operation; a trial list of possible isometric transformations is provided by the group of symmetry operators in the parent structure, which is used to generate all configurations via atomic substitutions. We have adapted the equations for configurational statistics to operate in the reduced configurational space of the independent configurations. Each configuration in this space is characterized by its reduced energy, which includes not only its energy but also a contribution from its degeneracy in the complete configurational space, via an entropic term. The new computer program SOD (site-occupancy disorder) is presented, which performs this analysis in systems with arbitrary symmetry and any size of supercell. As a case study we use the distribution of cations in iron antimony oxide FeSbO{sub 4}, where we also introduce some general considerations for the modelling of site-occupancy disorder in paramagnetic systems.

  17. First-principles study of structural and elastic properties of monoclinic and orthorhombic BiMnO3

    International Nuclear Information System (INIS)

    Mei Zhigang; Shang Shunli; Wang Yi; Liu Zikui

    2010-01-01

    The structural and elastic properties of BiMnO 3 with monoclinic (C 2/c) and orthorhombic (Pnma) ferromagnetic (FM) structures have been studied by first-principles calculations within LDA + U and GGA + U approaches. The equilibrium volumes and bulk moduli of BiMnO 3 phases are evaluated by equation of state (EOS) fittings, and the bulk properties predicted by LDA + U calculations are in better agreement with experiment. The orthorhombic phase is found to be more stable than the monoclinic phase at ambient pressure. A monoclinic to monoclinic phase transition is predicted to occur at a pressure of about 10 GPa, which is ascribed to magnetism versus volume instability of monoclinic BiMnO 3 . The single-crystal elastic stiffness constants c ij s of the monoclinic and orthorhombic phases are investigated using the stress-strain method. The c 46 of the monoclinic phase is predicted to be negative. In addition, the polycrystalline elastic properties including bulk modulus, shear modulus, Young's modulus, bulk modulus-shear modulus ratio, Poisson's ratio, and elastic anisotropy ratio are determined based on the calculated elastic constants. The presently predicted phase transition and elastic properties open new directions for investigation of the phase transitions in BiMnO 3 , and provide helpful guidance for the future elastic constant measurements.

  18. Molecular symmetry and spectroscopy

    CERN Document Server

    Bunker, Philip; Jensen, Per

    2006-01-01

    The first edition, by P.R. Bunker, published in 1979, remains the sole textbook that explains the use of the molecular symmetry group in understanding high resolution molecular spectra. Since 1979 there has been considerable progress in the field and a second edition is required; the original author has been joined in its writing by Per Jensen. The Material of the first edition has been reorganized and much has been added. The molecular symmetry group is now introduced early on, and the explanation of how to determine nuclear spin statistical weights has been consolidated in one chapter, after groups, symmetry groups, character tables and the Hamiltonian have been introduced. A description of the symmetry in the three-dimensional rotation group K(spatial), irreducible spherical tensor operators, and vector coupling coefficients is now included. The chapters on energy levels and selection rules contain a great deal of material that was not in the first edition (much of it was undiscovered in 1979), concerning ...

  19. Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

    Science.gov (United States)

    Seiler, Christian; Evers, Ferdinand

    2016-10-01

    A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

  20. Introductory group theory and its application to molecular structure

    CERN Document Server

    Ferraro, John R

    1975-01-01

    The success of the first edition of this book has encouraged us to revise and update it. In the second edition we have attempted to further clarify por­ tions of the text in reference to point symmetry, keeping certain sections and removing others. The ever-expanding interest in solids necessitates some discussion on space symmetry. In this edition we have expanded the discus­ sion on point symmetry to include space symmetry. The selection rules in­ clude space group selection rules (for k = 0). Numerous examples are pro­ vided to acquaint the reader with the procedure necessary to accomplish this. Recent examples from the literature are given to illustrate the use of group theory in the interpretation of molecular spectra and in the determination of molecular structure. The text is intended for scientists and students with only a limited theoretical background in spectroscopy. For this reason we have presented detailed procedures for carrying out the selection rules and normal coor­ dinate treatment of ...

  1. Nucleation in stress-induced tetragonal-monoclinic transformation of constrained zirconia

    International Nuclear Information System (INIS)

    Chan, S.K.

    1992-08-01

    A theory for stress-induced tetragonal→monoclinic transformation of constrained zirconia is presented based on the assumption that when forcibly strained to a regime of absolute instability where the free energy density of the tetragonal phase has a negative curvature, the constrained tetragonal zirconia becomes unstable with respect to the development of a modulated strain pattern that will evolve into a band of twin monoclinic domains. The temperature range for such an instability, the critical size of the inclusion, the corresponding critical strain, and the periodicity of the modulation are derived in terms of parameters that can be related to the elastic stiffness coefficients of various orders of the inclusion and the shear modulus of the host matrix. An entirely different mechanism is suggested for the reverse monoclinic→tetragonal transformation because the monoclinic phase is metastable when the extrinsic stress is removed. Estimates for the parameters are inferred from a variety of experimental data for pure zirconia and the numerical values for the predicted physical quantities are obtained

  2. Quasigroup of local-symmetry transformations in constrained theories

    International Nuclear Information System (INIS)

    Chitaya, N.P.; Gogilidze, S.A.; Surovtsev, Yu.S.

    1996-01-01

    In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated in the general case without restrictions on the algebra of constraints. The method of constructing the generator of local-symmetry transformations is obtained from the requirement for them to map the solutions of the Hamiltonian equations of motion into the solutions of the same equations. It is proved that second-class constraints do not contribute to the transformation law of the local symmetry entirely stipulated by all the first-class constraints (only by them) of an equivalent set passing to which from the initial constraint set is always possible and is presented. A mechanism of occurrence of higher derivatives of coordinates and group parameters in the symmetry transformation law in the Noether second theorem is elucidated. In the latter case it is shown that the obtained transformations of symmetry are canonical in the extended (by Ostrogradsky) phase space. It is thereby shown in the general case that the degeneracy of theories with the first- and second-class constraints is due to their invariance under local-symmetry transformations. It is also shown in the general case that the action functional and the corresponding Hamiltonian equations of motion are invariant under the same quasigroup of local-symmetry transformations. 29 refs

  3. Symmetry breaking in gauge glasses

    International Nuclear Information System (INIS)

    Hansen, K.

    1988-09-01

    In order to explain why nature selects the gauge groups of the Standard Model, Brene and Nielsen have proposed a way to break gauge symmetry which does not rely on the existence of a Higgs field. The observed gauge groups will in this scheme appear as the only surviving ones when this mechanism is applied to a random selection of gauge groups. The essential assumption is a discrete space-time with random couplings. Some working assumptions were made for computational reasons of which the most important is that quantum fluctuations were neclected. This work presents an example which under the same conditions show that a much wider class of groups than predicted by Brene and Nielsen will be broken. In particular no possible Standard Model Group survives unbroken. Numerical calculations support the analytical result. (orig.)

  4. Phase coexistence in ferroelectric solid solutions: Formation of monoclinic phase with enhanced piezoelectricity

    Directory of Open Access Journals (Sweden)

    Xiaoyan Lu

    2016-10-01

    Full Text Available Phase morphology and corresponding piezoelectricity in ferroelectric solid solutions were studied by using a phenomenological theory with the consideration of phase coexistence. Results have shown that phases with similar energy potentials can coexist, thus induce interfacial stresses which lead to the formation of adaptive monoclinic phases. A new tetragonal-like monoclinic to rhombohedral-like monoclinic phase transition was predicted in a shear stress state. Enhanced piezoelectricity can be achieved by manipulating the stress state close to a critical stress field. Phase coexistence is universal in ferroelectric solid solutions and may provide a way to optimize ultra-fine structures and proper stress states to achieve ultrahigh piezoelectricity.

  5. Generalizations of the BMS group and results

    International Nuclear Information System (INIS)

    Melas, E

    2006-01-01

    The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. In particular, the generalization B(2, 2) appropriate to the ultrahyperbolic signature (+, +, -, -) has been described in detail, and the study of its irreducible unitary representations (IRs) has been initiated. The infinite little groups of B(2, 2) have been given explicitly but its finite little groups have only been partially described. All the information needed in order to construct the finite little groups is given. Possible connections with gravitational instantons are being put forward

  6. Symmetry rules How science and nature are founded on symmetry

    CERN Document Server

    Rosen, Joe

    2008-01-01

    When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. In fact, modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. It is shown that the Universe cannot possess exact symmetry, which is a principle of fundamental significance. Curie's principle - which states that the symmetry of the effect is at least that of the cause - features prominently. An introduction to group theory, the mathematical language of symmetry, is included. This book will convince all interested readers of the importance of symmetry in science. Furthermore, it will serve as valuable background reading for all students in the physical sciences.

  7. Quantum group symmetry of classical and noncommutative geometry

    Indian Academy of Sciences (India)

    Debashish Goswami

    2016-07-01

    Jul 1, 2016 ... universal enveloping algebra U(L) of a Lie algebra L, (iv) ... Kustermans defined locally compact quantum groups too. .... There are other versions of quantum isometries formulated by me ..... classical connected spaces when either the space is ..... Etingof-Walton's paper, we have : (i) M0 is open and dense,.

  8. Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions

    International Nuclear Information System (INIS)

    Ryu, S.; Furusaki, A.; Ludwig, A.W.W.; Mudry, C.

    2007-01-01

    We extend the analysis of the conductance fluctuations in disordered metals by Altshuler, Kravtsov, and Lerner (AKL) to disordered superconductors with broken time-reversal symmetry in d=(2+ε) dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NLσM) we compute the anomalous scaling dimensions of the dominant scalar operators with 2s gradients to one-loop order. We show that, in analogy with the result of AKL for ordinary, metallic systems (Wigner-Dyson classes), an infinite number of high-gradient operators would become relevant (in the renormalization group sense) near two dimensions if contributions beyond one-loop order are ignored. We explore the possibility to compare, in symmetry class D, the ε=(2-d) expansion in d<2 with exact results in one dimension. The method we use to perform the one-loop renormalization analysis is valid for general symmetric spaces of Kaehler type, and suggests that this is a generic property of the perturbative treatment of NLσMs defined on Riemannian symmetric target spaces

  9. A generalized Wigner function for quantum systems with the SU(2) dynamical symmetry group

    International Nuclear Information System (INIS)

    Klimov, A B; Romero, J L

    2008-01-01

    We introduce a Wigner-like quasidistribution function to describe quantum systems with the SU(2) dynamic symmetry group. This function is defined in a three-dimensional group manifold and can be used to represent the states defined in several SU(2) invariant subspaces. The explicit differential Moyal-like form of the star product is found and analyzed in the semiclassical limit

  10. Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations

    International Nuclear Information System (INIS)

    Anco, S.C.; Bluman, G.

    1997-01-01

    Nonlocal symmetries are obtained for Maxwell's equations in three space-time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the constants of motion arising from local conservation laws for space-time symmetries. These nine constants of motion represent additional conserved quantities for the electromagnetic field in three space endash time dimensions. copyright 1997 American Institute of Physics

  11. q-deformed phase-space and its lattice structure

    International Nuclear Information System (INIS)

    Wess, J.

    1998-01-01

    Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are non-commutative spaces that inherit a well-defined mathematical structure from the quantum group symmetry. In turn, such quantum spaces can be interpreted as non-commutative configuration spaces for physical systems. We study the non-commutative Euclidean space that is based on the quantum group SO q (3)

  12. Gauge symmetry from decoupling

    Directory of Open Access Journals (Sweden)

    C. Wetterich

    2017-02-01

    Full Text Available Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

  13. Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

    Science.gov (United States)

    Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

    2018-04-01

    This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

  14. Description of the atomic disorder (local order) in crystals by the mixed-symmetry method

    Science.gov (United States)

    Dudka, A. P.; Novikova, N. E.

    2017-11-01

    An approach to the description of local atomic disorder (short-range order) in single crystals by the mixed-symmetry method based on Bragg scattering data is proposed, and the corresponding software is developed. In defect-containing crystals, each atom in the unit cell can be described by its own symmetry space group. The expression for the calculated structural factor includes summation over different sets of symmetry operations for different atoms. To facilitate the search for new symmetry elements, an "atomic disorder expert" was developed, which estimates the significance of tested models. It is shown that the symmetry lowering for some atoms correlates with the existence of phase transitions (in langasite family crystals) and the anisotropy of physical properties (in rare-earth dodecaborides RB12).

  15. Power of the Poincare Group: Elucidating the Hidden Symmetries in Focal Conic Domains

    International Nuclear Information System (INIS)

    Alexander, Gareth P.; Chen, Bryan Gin-ge; Matsumoto, Elisabetta A.; Kamien, Randall D.

    2010-01-01

    Focal conic domains are typically the 'smoking gun' by which smectic liquid crystalline phases are identified. The geometry of the equally spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincare symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures, and tilt-grain boundaries.

  16. Symmetry rules. How science and nature are founded on symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Rosen, J.

    2008-07-01

    When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. In fact, modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. It is shown that the Universe cannot possess exact symmetry, which is a principle of fundamental significance. Curie's principle - which states that the symmetry of the effect is at least that of the cause - features prominently. An introduction to group theory, the mathematical language of symmetry, is included. This book will convince all interested readers of the importance of symmetry in science. Furthermore, it will serve as valuable background reading for all students in the physical sciences. (orig.)

  17. Quandles and topological pairs symmetry, knots, and cohomology

    CERN Document Server

    Nosaka, Takefumi

    2017-01-01

    This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles. More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to s...

  18. Surprises and pitfalls arising from (pseudo)symmetry

    International Nuclear Information System (INIS)

    Zwart, Peter H.; Grosse-Kunstleve, Ralf W.; Lebedev, Andrey A.; Murshudov, Garib N.; Adams, Paul D.

    2008-01-01

    The presence of pseudosymmetry can cause problems in structure determination and refinement. The relevant background and representative examples are presented. It is not uncommon for protein crystals to crystallize with more than a single molecule per asymmetric unit. When more than a single molecule is present in the asymmetric unit, various pathological situations such as twinning, modulated crystals and pseudo translational or rotational symmetry can arise. The presence of pseudosymmetry can lead to uncertainties about the correct space group, especially in the presence of twinning. The background to certain common pathologies is presented and a new notation for space groups in unusual settings is introduced. The main concepts are illustrated with several examples from the literature and the Protein Data Bank

  19. In search of symmetry lost

    CERN Multimedia

    Wilczek, Frank

    2004-01-01

    Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world (8 pages) Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).

  20. Brillouin-zone database on the Bilbao Crystallographic Server.

    Science.gov (United States)

    Aroyo, Mois I; Orobengoa, Danel; de la Flor, Gemma; Tasci, Emre S; Perez-Mato, J Manuel; Wondratschek, Hans

    2014-03-01

    The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.

  1. Symmetry and symmetry breaking in quantum mechanics; Symetrie et brisure de symetrie en mechanique quantique

    Energy Technology Data Exchange (ETDEWEB)

    Chomaz, Philippe [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)

    1998-12-31

    In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels us of thinking the Single to comprehend the Universal. Quantum Numbers, magic Numbers and Numbers sign the wave. The matter is vibration. To describe the music of the world one needs keys, measures, notes, rules and partition: one needs quantum mechanics. The particles reduce themselves not in material points as the scholars of the past centuries thought, but they must be conceived throughout the space, in the accomplishment of shapes of volumes. When Einstein asked himself whether God plays dice, there was no doubt among its contemporaries that if He exists He is a geometer. In a Nature reduced to Geometry, the symmetries assume their role in servicing the Harmony. The symmetries allow ordering the energy levels to make them understandable. They impose there geometrical rules to the matter waves, giving them properties which sometimes astonish us. Hidden symmetries, internal symmetries and newly conceived symmetries have to be adopted subsequently to the observation of some order in this world of Quanta. In turn, the symmetries provide new observables which open new spaces of observation 17 refs., 16 figs.

  2. On irreducible representations of the ultrahyperbolic BMS group

    International Nuclear Information System (INIS)

    McCarthy, Patrick J.; Melas, Evangelos

    2003-01-01

    The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. Here, the generalisation B(2,2) appropriate to the ultrahyperbolic signature (+,+,-,-) is described in detail, and the irreducible unitary representations (IRs) of B(2,2) are analysed. It is proved that all induced IRs of B(2,2) arise from IRs of compact 'little groups'. These little groups, which are closed subgroups of K=SO(2)xSO(2), are classified here in detail, with particular attention paid to those of infinite order

  3. Crystal-field energy level analysis for Nd{sup 3+} ions at the low symmetry C{sub 1} site in [Nd(hfa){sub 4}(H{sub 2}O)](N(C{sub 2}H{sub 5}){sub 4}) single crystals

    Energy Technology Data Exchange (ETDEWEB)

    Mech, Agnieszka; Gajek, Zbigniew [Institute of Low Temperature and Structure Research, Polish Academy Of Sciences, ulica Okolna 2, 54-422 Wroclaw (Poland); Karbowiak, Miroslaw [Faculty of Chemistry, University of Wroclaw, ulica F Joliot-Curie 14, 50-383 Wroclaw (Poland); Rudowicz, Czeslaw [Institute of Physics, Szczecin University of Technology, Aleja Piastow 17, 70-310 Szczecin (Poland)], E-mail: karb@wchuwr.pl

    2008-09-24

    Optical absorption measurements of Nd{sup 3+} ions in single crystals of [Nd(hfa){sub 4}(H{sub 2}O)](N(C{sub 2}H{sub 5}){sub 4}) (hfa = hexafluoroacetyloacetonate), denoted Nd(hfa) for short, have been carried out at 4.2 and 298 K. This compound crystallizes in the monoclinic system (space group P 2{sub 1}/n). Each Nd ion is coordinated to eight oxygen atoms that originate from the hexafluoroacetylacetonate ligands and one oxygen atom from the water molecule. A total of 85 experimental crystal-field (CF) energy levels arising from the Nd{sup 3+} (4f{sup 3}) electronic configuration were identified in the optical spectra and assigned. A three-step CF analysis was carried out in terms of a parametric Hamiltonian for the actual C{sub 1} symmetry at the Nd{sup 3+} ion sites. In the first step, a total of 27 CF parameters (CFPs) in the Wybourne notation B{sub kq}, admissible by group theory, were determined in a preliminary fitting constrained by the angular overlap model predictions. The resulting CFP set was reduced to 24 specific independent CFPs using appropriate standardization transformations. Optimizations of the second-rank CFPs and extended scanning of the parameter space were employed in the second step to improve reliability of the CFP sets, which is rather a difficult task in the case of no site symmetry. Finally, seven free-ion parameters and 24 CFPs were freely varied, yielding an rms deviation between the calculated energy levels and the 85 observed ones of 11.1 cm{sup -1}. Our approach also allows prediction of the energy levels of Nd{sup 3+} ions that are hidden in the spectral range overlapping with strong ligand absorption, which is essential for understanding the inter-ionic energy transfer. The orientation of the axis system associated with the fitted CF parameters w.r.t. the crystallographic axes is established. The procedure adopted in our calculations may be considered as a general framework for analysis of CF levels of lanthanide ions at low

  4. Classical mirror symmetry

    CERN Document Server

    Jinzenji, Masao

    2018-01-01

    This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construct...

  5. Internal space decimation for lattice gauge theories

    International Nuclear Information System (INIS)

    Flyvbjerg, H.

    1984-01-01

    By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed. (orig.)

  6. Internal Einstein spaces and symmetry breaking

    International Nuclear Information System (INIS)

    Coquereaux, R.

    1984-01-01

    We first define a generalised gauge invariant Yang-Mills Lagrangian: the Killing metric -Ksub(αβ) on the group is replaced by a more general metric hsub(αβ)(x); the field hsub(αβ)(x) -a scalar from the space time point of view- is then covariantly coupled to the gauge field Asub(μ)sup(α) and is also self-coupled via a natural scalar potential (no parameters). Non trivial saddle points of this scalar potential, correspond to non standard Einstein metrics on the group C. the associated shifts lead to an entirely computable mass spectrum for the gauge field

  7. The monoclinic superstructure of the M2Pt6Al15 series (M=Ca, Sc, Y, La, Lu)

    International Nuclear Information System (INIS)

    Radzieowski, Mathis; Stegemann, Frank; Hoffmann, Rolf-Dieter; Janka, Oliver; Oldenburg Univ.

    2017-01-01

    The five ternary intermetallic compounds M 2 Pt 6 Al 15 (M=Ca, Sc, Y, La, Lu) were prepared from the elements by arc-melting. The crystal structure was determined via single crystal X-ray diffraction. The title compounds crystallize in a superstructure of the RE 0.67 Pt 2 Al 5 type structure (P6 3 /mmc) in the monoclinic crystal system with space group P12 1 /m1 (Sc 2 Pt 6 Al 15 : a=734.19(2), b=1628.96(10), c=734.19(2) pm, β=119.999(3) ; wR=0.0356, 3034 F 2 values, 68 variables). The superstructure can be derived by the superspace formalism using (3+2)D or (3+1)D interpretations of the diffraction data. The structural relation to the subcell structure is discussed on the basis of a group-subgroup scheme. In the crystal structure strongly bonded [Pt 2 Al 4 ] δ- slabs are alternatingly stacked with ordered layers containing M atoms and Al 3 triangles.

  8. Geometrical spin symmetry and spin

    International Nuclear Information System (INIS)

    Pestov, I. B.

    2011-01-01

    Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.

  9. G2 holonomy, mirror symmetry and phases of N = 1 SYM

    International Nuclear Information System (INIS)

    Hosomichi, Kazuo; Page, David C.

    2005-01-01

    We study the phase structure of four-dimensional N = 1 super Yang-Mills theories realized on D6-branes wrapping the RP 3 of a Z 2 orbifold of the deformed conifold. The non-trivial fundamental group of RP 3 allows for the gauge group to be broken to various product groups by Z 2 Wilson lines. We study the classical moduli space of theories in various pictures related by dualities including an M-theory lift. The quantum moduli space is analyzed in a dual IIB theory, where a complex curve contained in the target space plays a key role. We find that the quantum moduli space is made up of several branches, characterized by the presence or absence of a low energy U(1) gauge symmetry, which are connected at points of monopole condensation. The resulting picture of the quantum moduli space shows how the various gauge theories with different product gauge groups are connected to one another

  10. Symmetries in nature

    International Nuclear Information System (INIS)

    Mainzer, K.

    1988-01-01

    Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs

  11. Symmetries in nature

    Energy Technology Data Exchange (ETDEWEB)

    Mainzer, K

    1988-05-01

    Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs.

  12. An experimental study of symmetry lowering of analcime

    Science.gov (United States)

    Sugano, Neo; Kyono, Atsushi

    2018-04-01

    Single crystals of analcime were hydrothermally synthesized from a gel of analcime composition at 200 °C for 24 h. They were grown up to 100 μm in size with typical deltoidal icositetrahedron habit. The chemical composition determined by EPMA and TG analyses was Na0.84(Al0.89Si2.12)O6·1.04H2O. The single-crystal X-ray diffraction method was used to determine the symmetry and crystal structure of analcime. The analcime grown from a gel crystallized in cubic space group Ia3 d with lattice parameter a = 13.713(3) Å. In the cubic analcime, Si and Al cations were totally disordered over the framework T sites with site occupancy of Si:Al = 0.6871:0.3129(14). The single crystals of analcime with cubic symmetry were hydrothermally reheated at 200 °C in ultrapure water. After the hydrothermal treatment for 24 h, forbidden reflections for the cubic Ia3 d symmetry were observed. The reflection conditions led to an orthorhombic space group Ibca with lattice parameters a = 13.727(2) Å, b = 13.707(2) Å, and c = 13.707(2) Å. The unit-cell showed a slight distortion with ( a + b)/2 > c, yielding a flattened cell along c. In the orthorhombic analcime, Al exhibited a site preference for T11 site, which indicates that the Si/Al ordering over the framework T sites lowers the symmetry from cubic Ia3 d to orthorhombic Ibca. After the hydrothermal treatment for 48 h, reflections corresponding to orthorhombic space group Ibca were observed as well. The lattice parameters were a = 13.705(2) Å, b = 13.717(2) Å, and c = 13.706(2) Å, retaining the flattened cell shape with ( a + b)/2 > c. The Si and Al cations were further ordered among the framework T sites than the case of the hydrothermal treatment for 24 h. As a consequence, the Si/Al ordering was slightly but significantly accelerated with increasing the hydrothermal treatment time. During the hydrothermal reaction, however, chemical compositions were almost unchanged. The site occupancies of Na over the extra-framework sites

  13. A new technique for quantifying symmetry and opening angles in quartz c-axis pole figures: Implications for interpreting the kinematic and thermal properties of rocks

    Science.gov (United States)

    Hunter, N. J. R.; Weinberg, R. F.; Wilson, C. J. L.; Law, R. D.

    2018-07-01

    Variations in flow kinematics influence the type of crystallographic preferred orientations (CPOs) in plastically deformed quartz, yet we currently lack a robust means of quantifying the diagnostic symmetries that develop in the c-axis (0001) pole figure. In this contribution, we demonstrate how the symmetry of common c-axis topologies may be quantified by analysing the intensity distribution across a line transect of the pole figure margin. A symmetry value (S) measures the relative difference in intensities between marginal girdle maxima in the pole figure, and thus the degree to which the pole figure defines orthorhombic or monoclinic end member symmetries. This provides a semi-quantitative depiction of whether the rocks underwent coaxial or non-coaxial flow, respectively, and may subsequently be used to quantify other topological properties, such as the opening angle of girdle maxima. The open source Matlab® toolbox MTEX is used to quantify pole figure symmetries in quartzite samples from the Main Central Thrust (NW Himalaya) and the Moine Thrust (NW Scotland).

  14. Fluency over the monoclinic zirconia indentation

    International Nuclear Information System (INIS)

    Pereira, A.S.; Jornada, J.A.H. da

    1992-01-01

    It was investigated the environment and the time dependence of the Vickers microhardness of monoclinic zirconia single-crystals. The samples were kept at room temperature and the identifications were performed for different environments (air, toluene and water). An indentation creep process was observed for the samples indented is moist media, indicating for a water activated plastic relaxation mechanism. The possible influence of such effect in the fatigue and phase transformations mechanisms of zirconia based ceramics is discussed. (author)

  15. Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections

    Science.gov (United States)

    Chen, Lan; Sun, Hongwei; Lai, Chengming

    2015-01-01

    There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…

  16. The quantum symmetry of rational conformal field theories

    Directory of Open Access Journals (Sweden)

    César Gómez

    1991-04-01

    Full Text Available The quantum group symmetry of the c ˇ1 Rational Conformal Field Theory, in its Coulomb gas version, is formulated in terms of a new type of screened vertex operators, which define the representation spaces of a quantum group Q. The conformal properties of these operators show a deep interplay between the quantum group Q and the Virasoro algebra.The R-matrix, the comultiplication rules and the quantum Clebsch-Gordan coefficients of Q are obtained using contour deformation techniques. Finally, the relation between the chiral vertex operators and the quantum Clebsch-Gordan coefficients is shown.

  17. Galileo symmetries in polymer particle representation

    International Nuclear Information System (INIS)

    Chiou, D-W

    2007-01-01

    To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic particle as a simple toy model. The complete Galileo transformations (translation, rotation and Galileo boost) are naturally defined in the polymer particle Hilbert space and Galileo symmetries are recovered with highly suppressed deviations in the low-energy regime from the underlying polymer particle description

  18. Geometric modular action and transformation groups

    International Nuclear Information System (INIS)

    Summers, S.J.

    1996-01-01

    We study a weak form of geometric modular action, which is naturally associated with transformation groups of partially ordered sets and which provides these groups with projective representations. Under suitable conditions it is shown that these groups are implemented by point transformations of topological spaces serving as models for space-times, leading to groups which may be interpreted as symmetry groups of the space-times. As concrete examples, it is shown that the Poincare group and the de Sitter group can be derived from this condition of geometric modular action. Further consequences and examples are discussed. (orig.)

  19. Real-space multiple-scattering theory and the electronic structure of systems with full or reduced symmetry

    International Nuclear Information System (INIS)

    Zhang, X.; Gonis, A.; MacLaren, J.M.

    1989-01-01

    We present a new real-space multiple-scattering-theory method for the solution of the Schroedinger equation and the calculation of the electronic structure of solid materials with full or reduced symmetry. The method is based on the concept of semi-infinite periodicity (SIP), rather than translational invariance, and on the property of removal invariance of the scattering matrix of systems with SIP. This latter property allows one to replace the usual Brillouin-zone integrals in reciprocal space by a self-consistency equation for the t matrix, which is sufficient for the determination of the Green function and related properties. Because it is developed entirely in direct space, the method provides a unified treatment of the electronic structure of bulk materials, surfaces, interfaces and grain boundaries (coherent or incoherent), impurities of interstitial or substitutional kinds, and can be easily extended to treat concentrated, substitutionally disordered alloys. One of its advantages over methods based on Bloch's theorem and reciprocal space is the great simplicity of setting up and running the associated computer codes even for complex structures, and structures with reduced or no symmetry that lie outside the realm of applicability of conventional methods. We present the results of model calculations for one-dimensional and three-dimensional model systems as well as for three-dimensional realistic materials. Where appropriate, these results are compared with those obtained through conventional techniques, and give an indication of the method's flexibility and reliability. Our applications of this method to this point are discussed, and our plans for future development are presented

  20. Quantum spaces, central extensions of Lie groups and related quantum field theories

    Science.gov (United States)

    Poulain, Timothé; Wallet, Jean-Christophe

    2018-02-01

    Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.

  1. Dynamical symmetry breaking of the electroweak interactions and the renormalization group

    International Nuclear Information System (INIS)

    Hill, C.T.

    1990-08-01

    We discuss dynamical symmetry breaking with an emphasis on the renormalization group as the key tool to obtaining reliable predictions. In particular we discuss the mechanism for breaking the electroweak interactions which relies upon the formation of condensates involving the conventional quarks and leptons. Such a scheme indicates that the top quark is heavy, greater than or of order 200 GeV, and gives further predictions for the Higgs boson mass. We also briefly describe recent attempts to incorporate a 4th generation in a more natural scheme. 13 refs., 3 figs., 1 tab

  2. Molecular symmetry and group theory a programmed introduction to chemical applications

    CERN Document Server

    Vincent, Alan

    2013-01-01

    This substantially revised and expanded new edition of the bestselling textbook, addresses the difficulties that can arise with the mathematics that underpins the study of symmetry, and acknowledges that group theory can be a complex concept for students to grasp.Written in a clear, concise manner, the author introduces a series of programmes that help students learn at their own pace and enable to them understand the subject fully. Readers are taken through a series of carefully constructed exercises, designed to simplify the mathematics and give them a full understanding of how this

  3. Two dimentional lattice vibrations from direct product representations of symmetry groups

    Directory of Open Access Journals (Sweden)

    J. N. Boyd

    1983-01-01

    two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.

  4. Dynamical systems with first- and second-class constraints. II. Local-symmetry transformations

    International Nuclear Information System (INIS)

    Chitaia, N.P.; Gogilidze, S.A.; Surovtsev, Y.S.

    1997-01-01

    In the framework of the generalized Hamiltonian formalism by Dirac, local symmetries of dynamical systems with first- and second-class constraints are investigated. The method of constructing the generator of local-symmetry transformations is presented both for theories with an algebra of constraints of a special form (a majority of the physically interesting theories) and in the general case without restrictions on the algebra of constraints. It is proven that second-class constraints do not contribute to the transformation law of the local symmetry entirely stipulated by all the first-class constraints. A mechanism of the occurrence of higher derivatives of coordinates and group parameters in the symmetry transformation law in Noether close-quote s second theorem is elucidated. In the latter case it is shown that the obtained transformations of symmetry are canonical in the extended (by Ostrogradsky) phase space. It is thereby shown that in the general case the degeneracy of theories with first- and second-class constraints is due to their invariance under local-symmetry transformations. copyright 1997 The American Physical Society

  5. Symmetry mappings concomitant to particle-number-conservation-baryon-number conservation

    International Nuclear Information System (INIS)

    Davis, W.R.

    1977-01-01

    Four theorem serve to demonstrate that matter fields in space-time admit certain timelike symmetry mappings concomitant to the familiar notion of particle number conservation, which can be more fundamentally accounted for by a type of projective invariance principle. These particular symmetry mappings include a family of symmetry properties that may be admitted by Riemannian space-times. In their strongest form, the results obtained provide some insight relating to the conservation of baryon number

  6. Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking

    Energy Technology Data Exchange (ETDEWEB)

    Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi [Kanazawa Univ., Inst. for Theoretical Physics, Kanazawa, Ishikawa (Japan)

    2000-04-01

    The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)

  7. Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking

    International Nuclear Information System (INIS)

    Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi

    2000-01-01

    The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)

  8. Nonlinear symmetry realizations and the generalized CP sup(n-1) model

    International Nuclear Information System (INIS)

    Santos, T.A.

    1982-01-01

    The genralized CP sup(n-1) model having U(p) as Gauge group in the two-dimension Euclidean space in the several existing formulations is presented. Such a model is described as a nonlinear symmetry realization which becames linear when restricted to a determined sub-groups treating therefore of fields which have values in the quocient space G/H. Classical instanton and meron solutions for this model are presented and the existence of a mechanism to generate a family of non auto-dual solutions with finite action, taking as starting point the instanton solutions, is demonstrated. (L.C.) [pt

  9. Rotational Symmetry Breaking in Baby Skyrme Models

    Science.gov (United States)

    Karliner, Marek; Hen, Itay

    We discuss one of the most interesting phenomena exhibited by baby skyrmions - breaking of rotational symmetry. The topics we will deal with here include the appearance of rotational symmetry breaking in the static solutions of baby Skyrme models, both in flat as well as in curved spaces, the zero-temperature crystalline structure of baby skyrmions, and finally, the appearance of spontaneous breaking of rotational symmetry in rotating baby skyrmions.

  10. Symmetries and Laplacians introduction to harmonic analysis, group representations and applications

    CERN Document Server

    Gurarie, D

    1992-01-01

    Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...

  11. Boson-fermion symmetries in the W-Pt region

    International Nuclear Information System (INIS)

    Warner, D.D.

    1985-01-01

    The concept of symmetry in the Interacting Boson Model (IBM) description of even-even nuclei has proved to be one of the model's most important elements, because they provide benchmarks in the formulation of a unified description of a broad range of nuclei. The importance of the recently proposed symmetries in odd-even systems can thus be viewed in the same light, and their role in pointing to a simple prescription for the changing collective structure in odd A nuclei throughout a major shell is likely to prove even more essential, given the much greater complexity of the boson-fermion (IBFM) Hamiltonian. The group structure of a boson-fermion system is described by U/sup B/(6) x U/sup F/(m) where m specifies the number of states available to the odd fermion, and thus depends on the single particle space assumed. The ability to construct group chains corresponding to the symmetries SU(5), SU(3) or 0(6) depends on the value of m. Of the structures studied in detail to date, the case of m = 12 is the one with the broadest potential. The fermion is allowed to occupy orbits with j = 1/2, 3/2 and 5/2, so that the assumed single particle space corresponds to the negative parity states available to an odd neutron at the end of the N = 82-126 shell, namely, P/sub 1/2/, p/sub 3/2/ and f/sub 5/2/. The region of interest thus spans the W-Pt nuclei, and since one prerequisite for an odd-A symmetry is the existence of that same symmetry in the neighboring even-even core nucleus, the odd Pt nuclei around A = 196 offer the obvious testing ground for the 0(6) limit of U(6/12). The heavier even-even W nuclei, on the other hand, have the characteristics of an axial rotor, and hence the negative parity structure of the neighboring odd W isotopes offers the possibility to study the validity of the SU(3) limit. Given a definition and understanding of these two limits, the construction of a simple description of the transitional Os nuclei can be considered

  12. The crystal structure of bøgvadite (Na2SrBa2Al4F20)

    DEFF Research Database (Denmark)

    Balic Zunic, Tonci

    2014-01-01

    The crystal structure of bøgvadite, Na2SrBa2Al4F20, has been solved and refined to a R1 factor of 4.4% from single-crystal data (MoKα X-ray diffraction, CCD area detector) on a sample from the cryolite deposit at Ivittuut, SW Greenland. Bøgvadite is monoclinic, P21/n space group, with unit cell...... parameters a= 7.134(1), b= 19.996(3) and c= 5.3440(8) Å, β = 90.02(1)o. A close proximity of the crystal structure to an orthorhombic symmetry and the presence of the two twin components in a nearly 1:1 ratio suggest that the investigated bøgvadite crystal has originally formed as a high......-temperature orthorhombic polymorph which on cooling transformed to the stable low temperature monoclinic structure. The bøgvadite crystal structure has groupings of cation-fluoride coordination polyhedra similar to those found in the crystal structures of the genetically closely associated minerals jarlite...

  13. Non-commutative covering spaces and their symmetries

    DEFF Research Database (Denmark)

    Canlubo, Clarisson

    dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using...... will explain this and relate it to bi-Galois theory.Using the OZ-transform, we will show that non-commutative covering spaces come in pairs.Several categories of covering spaces will be dened and studied. Appealing to Tannaka duality,we will explain how this lead to a notion of an etale fundamental group...

  14. Symmetries and conservation laws of the damped harmonic oscillator

    Indian Academy of Sciences (India)

    We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...

  15. In situ TEM observation of the growth and decomposition of monoclinic W18O49 nanowires

    International Nuclear Information System (INIS)

    Chen, C L; Mori, H

    2009-01-01

    The growth of monoclinic W 18 O 49 nanowires by heat treatment of a tungsten filament at ∼873 K and the decomposition of these nanowires under 200 keV electron irradiation at ∼1023 K have been investigated using in situ transmission electron microscopy (TEM). In situ TEM observation of the growth confirmed the vapor-solid growth mechanism of the monoclinic W 18 O 49 nanowires. In situ irradiation experiments revealed the formation of metallic bcc tungsten from monoclinic W 18 O 49 nanowires under 200 keV electron irradiation.

  16. Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton

    International Nuclear Information System (INIS)

    Julia, B.

    1996-01-01

    General relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra A 1 (1) and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semi-direct product of Lie(A 1 (1) ) by the Witt algebra Lie(W). Furthermore we exhibit the corresponding hidden gauge symmetries. We show that the theory can be understood in terms of an infinite dimensional potential space involving all degrees of freedom: the dilaton as well as matter and gravitation. In the dilaton sector the linear system that extends the previously known Lax pair has the form of a twisted self-duality constraint that is the analog of the self-duality constraint arising in extended supergravities in higher space-time dimensions. Our results furnish a group theoretical explanation for the simultaneous occurrence of two spectral parameters, a constant one (=y) and a variable one (=t). They hold for all 2d non-linear σ-models that are obtained by dimensional reduction of G/H models in three dimensions coupled to pure gravity. (orig./WL) (orig.)

  17. Circular symmetry in topologically massive gravity

    International Nuclear Information System (INIS)

    Deser, S; Franklin, J

    2010-01-01

    We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null. (note)

  18. Circular symmetry in topologically massive gravity

    Energy Technology Data Exchange (ETDEWEB)

    Deser, S [Physics Department, Brandeis University, Waltham, MA 02454 (United States); Franklin, J, E-mail: deser@brandeis.ed, E-mail: jfrankli@reed.ed [Reed College, Portland, OR 97202 (United States)

    2010-05-21

    We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null. (note)

  19. A second monoclinic polymorph of 2-(3,5-dimethyl-1H-pyrazol-1-yl)-2-hy­droxy­imino-N′-[1-(pyridin-2-yl)ethyl­idene]acetohydrazide

    Science.gov (United States)

    Plutenko, Maxym O.; Lampeka, Rostislav D.; Haukka, Matti; Nordlander, Ebbe

    2013-01-01

    The title compound, C14H16N6O2, is a second monoclinic polymorph of 2-[1-(3,5-dimeth­yl)pyrazol­yl]-2-hy­droxy­imino-N′-[1-(2-pyrid­yl)ethyl­idene] acetohydrazide, with two crystallographically independent mol­ecules per asymmetric unit. The non-planar mol­ecules are chemically equal having similar geometric parameters. The previously reported polymorph [Plutenko et al. (2012 ▶). Acta Cryst. E68, o3281] was described in space group Cc (Z = 4). The oxime group and the O atom of the amide group are anti with respect to the C—C bond. In the crystal, mol­ecules are connected by N—H⋯N hydrogen bonds into zigzag chains extending along the b axis. PMID:23723911

  20. Symmetry and inflation

    International Nuclear Information System (INIS)

    Chimento, Luis P.

    2002-01-01

    We find the group of symmetry transformations under which the Einstein equations for the spatially flat Friedmann-Robertson-Walker universe are form invariant. They relate the energy density and the pressure of the fluid to the expansion rate. We show that inflation can be obtained from nonaccelerated scenarios by a symmetry transformation. We derive the transformation rule for the spectrum and spectral index of the curvature perturbations. Finally, the group is extended to investigate inflation in the anisotropic Bianchi type-I spacetime and the brane-world cosmology

  1. Quantum group symmetries and completeness for \\boldsymbol {A}_{\\boldsymbol {2n}}^{\\boldsymbol{(2)}} open spin chains

    Science.gov (United States)

    Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang

    2017-07-01

    We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

  2. Symmetry chains for the atomic shell model. I. Classification of symmetry chains for atomic configurations

    International Nuclear Information System (INIS)

    Gruber, B.; Thomas, M.S.

    1980-01-01

    In this article the symmetry chains for the atomic shell model are classified in such a way that they lead from the group SU(4l+2) to its subgroup SOsub(J)(3). The atomic configurations (nl)sup(N) transform like irreducible representations of the group SU(4l+2), while SOsub(J)(3) corresponds to total angular momentum in SU(4l+2). The defining matrices for the various embeddings are given for each symmetry chain that is obtained. These matrices also define the projection onto the weight subspaces for the corresponding subsymmetries and thus relate the various quantum numbers and determine the branching of representations. It is shown in this article that three (interrelated) symmetry chains are obtained which correspond to L-S coupling, j-j coupling, and a seniority dependent coupling. Moreover, for l<=6 these chains are complete, i.e., there are no other chains but these. In articles to follow, the symmetry chains that lead from the group SO(8l+5) to SOsub(J)(3) will be discussed, with the entire atomic shell transforming like an irreducible representation of SO(8l+5). The transformation properties of the states of the atomic shell will be determined according to the various symmetry chains obtained. The symmetry lattice discussed in this article forms a sublattice of the larger symmetry lattice with SO(8l+5) as supergroup. Thus the transformation properties of the states of the atomic configurations, according to the various symmetry chains discussed in this article, will be obtained too. (author)

  3. Electric-magnetic duality as a secondary symmetry

    International Nuclear Information System (INIS)

    Brandt, R.A.; Young, K.

    1980-01-01

    In both the abelian and non-abelian classical point magnetic monopole theories, electric current conservation is a consequence of gauge invariance, but, since there is no magnetic gauge group, magnetic current conservation is not a Noether-type conservation law. In the abelian models, the equations of motion (but not the lagrangian) are invariant to the duality rotations in electric-magnetic charge space, but this is not the case in the non-abelian models. In an attempt to understand these and related points, we introduce a generalization of Noether's theorem. Consider a physical system described by a set of variables THETA and characterized by a lagrangian density L(THETA). A transormation law THETA → G THETA which leaves L invariant leads to a conserved current Jsub(μ)(THETA). We then call G a primary symmetry. A second transformation law THETA → D THETA which leaves the equations of motion, but not L, invariant then leads to another conserved current Jsub(μ)(D THETA). We then call D a secondary symmetra. Our main point is that Jsub(μ) (D THETA) may be conserved even if the equations of motion are not invariant under D. All that is required is that the change of the equations of motion under D is perpendicular (in the field space) to the change of the fields under G. Then we call D an incomplete secondary symmetry. We show that in both the abelian and non-abelian monopole theories, duality is an incomplete secondary symmetry whose associated conservation law is magnetic current conservation. Thus it is the interpretation of duality as a secondary symmetry which explains magnetic current conservation and which generalizes from the abelian theories to the non-abelian ones. This suggests that magnetic current conservation may remain valid in quantum field theory. (orig.)

  4. Shape analysis with subspace symmetries

    KAUST Repository

    Berner, Alexander

    2011-04-01

    We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising. © 2010 The Author(s).

  5. Discrete symmetries in the MSSM

    Energy Technology Data Exchange (ETDEWEB)

    Schieren, Roland

    2010-12-02

    The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)

  6. Discrete symmetries in the MSSM

    International Nuclear Information System (INIS)

    Schieren, Roland

    2010-01-01

    The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z R 4 symmetry is discovered which solves the μ-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z R 4 is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z R 4 symmetry and other desirable features. (orig.)

  7. Soliton surfaces associated with generalized symmetries of integrable equations

    International Nuclear Information System (INIS)

    Grundland, A M; Post, S

    2011-01-01

    In this paper, based on the Fokas et al approach (Fokas and Gel'fand 1996 Commun. Math. Phys. 177 203-20; Fokas et al 2000 Sel. Math. 6 347-75), we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a Lie algebra using the formalism of generalized vector fields, their prolongation structure and links with the Frechet derivatives. We express the necessary and sufficient condition for the existence of such surfaces in terms of the invariance criterion for generalized symmetries and identify additional sufficient conditions which admit an explicit integration of the immersion functions of 2D surfaces in Lie algebras. We discuss in detail the su(N)-valued immersion functions generated by conformal symmetries of the CP N-1 sigma model defined on either the Minkowski or Euclidean space. We further show that the sufficient conditions for explicit integration of such immersion functions impose additional restrictions on the admissible conformal symmetries of the model defined on Minkowski space. On the other hand, the sufficient conditions are identically satisfied for arbitrary conformal symmetries of finite action solutions of the CP N-1 sigma model defined on Euclidean space.

  8. SIMS study of oxygen diffusion in monoclinic HfO2

    Science.gov (United States)

    Mueller, Michael P.; De Souza, Roger A.

    2018-01-01

    The diffusion of oxygen in dense ceramics of monoclinic HfO2 was studied by means of (18O/16O) isotope exchange annealing and subsequent determination of isotope depth profiles by Secondary Ion Mass Spectrometry. Anneals were performed in the temperature range of 573 ≤T /K ≤ 973 at an oxygen partial pressure of p O2=200 mbar . All measured isotope profiles exhibited two features: the first feature, closer to the surface, was attributed mainly to slow oxygen diffusion in an impurity silicate phase; the second feature, deeper in the sample, was attributed to oxygen diffusion in bulk monoclinic HfO2 . The activation enthalpy of oxygen tracer diffusion in bulk HfO2 was found to be ΔHD∗≈0.5 eV .

  9. Power of the Poincaré group: elucidating the hidden symmetries in focal conic domains.

    Science.gov (United States)

    Alexander, Gareth P; Chen, Bryan Gin-Ge; Matsumoto, Elisabetta A; Kamien, Randall D

    2010-06-25

    Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures, and tilt-grain boundaries.

  10. Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

    Science.gov (United States)

    Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

    2018-03-01

    In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

  11. Symmetry in Kaluza-Klein theory

    International Nuclear Information System (INIS)

    Strathdee, J.

    1982-12-01

    A method is described for making harmonic expansions on the internal space of a Kaluza-Klein vacuum in cases where this space is a coset space. This method fully exploits the symmetry of the space and should be useful for the analysis of excitation spectra and, in particular, for constructing the correct zero-mode ansatz in cases where the multi-dimensional gravitational fields are coupled to matter fields of various kinds. (author)

  12. FT-IR reflection spectra of single crystals: resolving phonons of different symmetry without using polarised radiation

    Directory of Open Access Journals (Sweden)

    METODIJA NAJDOSKI

    2000-07-01

    Full Text Available Fourier-transform infrared (FT-IR reflection spectra, asquired at nearnormal incidence, were recorded from single crystals belonging to six crystal systems: CsCr(SO42.12H2O (alum, cubic, K2CuCl2·2H2O (Mitscherlichite, tetragonal, CaCO3 (calcite, hexagonal, KHSO4 (mercallite, orthorhombic, CaSO4·2H2O (gypsum, monoclinic and CuSO4·5H2O (chalcantite, triclinic. The acquired IR reflection spectra were further transformed into absorption spectra, employing the Kramers-Kronig transformation. Except for the cubic alums, the spectra strongly depend on the crystal face from which they were recorded; this is a consequence of anisotropy. Phonons of a given symmetry (E-species, in tetragonal/hexagonal and B-species, in monoclinic crystals may be resolved without using a polariser. The spectrum may be simplified in the case of an orthorhombic crystal, as well. The longitudinal-optical (LO and transversal-optical (TO mode frequencies were calculated in the case of optically isotropic and the simplified spectra of optically uniaxial crystals.

  13. Spectroscopic studies of dynamically compacted monoclinic ZrO2

    NARCIS (Netherlands)

    Maczka, M.; Lutz, E.T.G.; Verbeek, H.J.; Oskam, K.; Meijerink, A.; Hanuza, J.; Stuivinga, M.E.C.

    1999-01-01

    The properties of dynamically compacted monoclinic zirconia have been studied by X-ray powder diffraction, IR, Raman, EPR and luminescence spectroscopy. Compaction introduces a large number of defects into the sample, which leads to a broadening of the X-ray lines, and IR and Raman bands. Besides,

  14. Quantum symmetry for pedestrians

    International Nuclear Information System (INIS)

    Mack, G.; Schomerus, V.

    1992-03-01

    Symmetries more general than groups are possible in quantum therory. Quantum symmetries in the narrow sense are compatible with braid statistics. They are theoretically consistent much as supersymmetry is, and they could lead to degenerate multiplets of excitations with fractional spin in thin films. (orig.)

  15. Dielectric tensor of monoclinic Ga2O3 single crystals in the spectral range 0.5–8.5 eV

    Directory of Open Access Journals (Sweden)

    C. Sturm

    2015-10-01

    Full Text Available The dielectric tensor of Ga2O3 in the monoclinic (β phase was determined by generalized spectroscopic ellipsometry in a wide spectral range from 0.5 eV to 8.5 eV as well as by density functional theory calculations combined with many-body perturbation theory including quasiparticle and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to |εxz| ≈ 0.30 and cannot be neglected. Even in the transparent spectral range where it is quite small (|εxz| < 0.02 it causes a rotation of the dielectric axes around the symmetry axis of up to 20°.

  16. Hidden Symmetries for Thermodynamics and Emergence of Relativity

    International Nuclear Information System (INIS)

    Zhao Liu

    2010-01-01

    Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment on some of the problems of Verlinde's proposal with special emphasis on the thermodynamical origin of the principle of relativity. It is found that there is a large group of hidden symmetries of thermodynamics, which contains the Poincare group of the spacetime for which space is emergent. This explains the thermodynamic origin of the principle of relativity. (general)

  17. Study of the cubic - to - monoclinic transformation in magnesia partially stabilized zirconia

    International Nuclear Information System (INIS)

    Muccillo, R.

    1988-01-01

    The transformation of the cubic phase to the stable monoclinic phase in ZrO 2 : 3%MgO quenched from 1450 0 C to RT has been studied by X-ray diffractometry in order to explain the thermal hysteresis in the electrical conductivity. The monoclinic-to-cubic ratio has been measured for samples annealed in the 500 0 C-1000 0 C temperature range. The results show that the decrease in the cubic phase content is the main responsible for the thermal hysteresis in the electrical conductivity of the magnesia partially stabilized zirconia solid electrolytes. (author) [pt

  18. Syntheses, spectroscopic characterization, crystal structure and natural rubber vulcanization activity of new disulfides derived from sulfonyldithiocarbimates

    Science.gov (United States)

    Alves, Leandro de Carvalho; Rubinger, Mayura Marques Magalhães; Tavares, Eder do Couto; Janczak, Jan; Pacheco, Elen Beatriz Acordi Vasques; Visconte, Leila Lea Yuan; Oliveira, Marcelo Ribeiro Leite

    2013-09-01

    The compounds (Bu4N)2[(4-RC6H4SO2NCS2)2] [Bu4N = tetrabutylammonium cation; R = H (1), F (2), Cl (3) and Br (4)] and (Ph4P)2[(4-RC6H4SO2NCS2)2]ṡH2O [Ph4P = tetraphenylphosphonium cation and R = I (5)] were synthesized by the reaction of the potassium dithiocarbimates (4-RC6H4SO2NCS2K2ṡ2H2O) with I2 and Bu4NBr or Ph4PCl. The IR data were consistent with the formation of the dithiocarbimatodisulfides anions. The NMR spectra showed the expected signals for the cations and anions in a 2:1 proportion. The structures of compounds 1-5 were determined by the single crystal X-ray diffraction. The compounds 2, 3 and 4 are isostructural and crystallise in the centrosymmetric space group C2/c of the monoclinic system. Compound 1 crystallises in the monoclinic system in the space group of P21/n and the compound 5 crystallises in the centrosymmetric space group P-1 of the triclinic system. The complex anions of compounds 2, 3 and 4 exhibit similar conformations having twofold symmetry, while in 1 and 5 the anions exhibit C1 symmetry. The activity of the new compounds in the vulcanization of the natural rubber was evaluated and compared to the commercial accelerators ZDMC, TBBS and TMTD. These studies confirm that the sulfonyldithiocarbimato disulfides anions are new vulcanization accelerators, being slower than the commercial accelerators, but producing a greater degree of crosslinking, and scorch time values compatible with good processing safety for industrial applications. The mechanical properties, stress and tear resistances were determined and compared to those obtained with the commercial accelerators.

  19. Discrete symmetries in the heterotic-string landscape

    International Nuclear Information System (INIS)

    Athanasopoulos, P

    2015-01-01

    We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N = (2, 2) model and we use this operator to construct a map between N = (2, 0) models. The landscape of N = (2, 0) models is of particular interest among all heterotic-string models for two important reasons: Firstly, N =1 spacetime SUSY requires (2, 0) superconformal invariance and secondly, models with the well motivated by the Standard Model SO(10) unification structure are of this type. This idea was inspired by a new discrete symmetry in the space of fermionic ℤ 2 × ℤ 2 heterotic-string models that exchanges the spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. We will describe how to generalize this to arbitrary internal rational Conformal Field Theories. (paper)

  20. Discrete symmetries in the heterotic-string landscape

    Science.gov (United States)

    Athanasopoulos, P.

    2015-07-01

    We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N = (2, 2) model and we use this operator to construct a map between N = (2, 0) models. The landscape of N = (2, 0) models is of particular interest among all heterotic-string models for two important reasons: Firstly, N =1 spacetime SUSY requires (2, 0) superconformal invariance and secondly, models with the well motivated by the Standard Model SO(10) unification structure are of this type. This idea was inspired by a new discrete symmetry in the space of fermionic ℤ2 × ℤ2 heterotic-string models that exchanges the spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. We will describe how to generalize this to arbitrary internal rational Conformal Field Theories.

  1. Noncommutative gauge theory and symmetry breaking in matrix models

    International Nuclear Information System (INIS)

    Grosse, Harald; Steinacker, Harold; Lizzi, Fedele

    2010-01-01

    We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3) c xSU(2) L xU(1) Q [resp. SU(3) c xU(1) Q ], which couples appropriately to all fields in the standard model. An additional U(1) B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

  2. The weak-scale hierarchy and discrete symmetries

    International Nuclear Information System (INIS)

    Haba, Naoyuki; Matsuoka, Takeo; Hattori, Chuichiro; Matsuda, Masahisa; Mochinaga, Daizo.

    1996-01-01

    In the underlying Planck scale theory, we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak-scale hierarchy under control. Under the discrete symmetry the μ-problem and the tadpole problem can be solved simultaneously without relying on some fine-tuning of parameters. Instead, it is required that doublet Higgs and color-triplet Higgs fields reside in different irreducible representations of the gauge symmetry group at the Planck scale and that they have distinct charges of the discrete symmetry group. (author)

  3. Symmetry breaking on density in escaping ants: experiment and alarm pheromone model.

    Directory of Open Access Journals (Sweden)

    Geng Li

    Full Text Available The symmetry breaking observed in nature is fascinating. This symmetry breaking is observed in both human crowds and ant colonies. In such cases, when escaping from a closed space with two symmetrically located exits, one exit is used more often than the other. Group size and density have been reported as having no significant impact on symmetry breaking, and the alignment rule has been used to model symmetry breaking. Density usually plays important roles in collective behavior. However, density is not well-studied in symmetry breaking, which forms the major basis of this paper. The experiment described in this paper on an ant colony displays an increase then decrease of symmetry breaking versus ant density. This result suggests that a Vicsek-like model with an alignment rule may not be the correct model for escaping ants. Based on biological facts that ants use pheromones to communicate, rather than seeing how other individuals move, we propose a simple yet effective alarm pheromone model. The model results agree well with the experimental outcomes. As a measure, this paper redefines symmetry breaking as the collective asymmetry by deducing the random fluctuations. This research indicates that ants deposit and respond to the alarm pheromone, and the accumulation of this biased information sharing leads to symmetry breaking, which suggests true fundamental rules of collective escape behavior in ants.

  4. At the origins of mass: elementary particles and fundamental symmetries

    International Nuclear Information System (INIS)

    Iliopoulos, Jean; Englert, Francois

    2015-01-01

    After a brief recall of the history of cosmology, the author proposes an overview of the different symmetries (symmetries in space and in time, internal symmetries, local or gauge symmetries), describes the mass issue (gauge interactions, quarks and leptons as matter mass constituents, chirality), addresses the spontaneous symmetry breaking (the Curie theorem, spontaneous symmetry breaking in classical physics and in quantum physics, the Goldstone theorem, spontaneous symmetry breaking in presence of gauge interactions), presents the standard theory (electromagnetic and weak interactions, strong interactions, relationship with experiment). An appendix presents elementary particles, and notably reports the story of the neutrino

  5. Exploiting Symmetry on Parallel Architectures.

    Science.gov (United States)

    Stiller, Lewis Benjamin

    1995-01-01

    This thesis describes techniques for the design of parallel programs that solve well-structured problems with inherent symmetry. Part I demonstrates the reduction of such problems to generalized matrix multiplication by a group-equivariant matrix. Fast techniques for this multiplication are described, including factorization, orbit decomposition, and Fourier transforms over finite groups. Our algorithms entail interaction between two symmetry groups: one arising at the software level from the problem's symmetry and the other arising at the hardware level from the processors' communication network. Part II illustrates the applicability of our symmetry -exploitation techniques by presenting a series of case studies of the design and implementation of parallel programs. First, a parallel program that solves chess endgames by factorization of an associated dihedral group-equivariant matrix is described. This code runs faster than previous serial programs, and discovered it a number of results. Second, parallel algorithms for Fourier transforms for finite groups are developed, and preliminary parallel implementations for group transforms of dihedral and of symmetric groups are described. Applications in learning, vision, pattern recognition, and statistics are proposed. Third, parallel implementations solving several computational science problems are described, including the direct n-body problem, convolutions arising from molecular biology, and some communication primitives such as broadcast and reduce. Some of our implementations ran orders of magnitude faster than previous techniques, and were used in the investigation of various physical phenomena.

  6. Poisson structure and symmetry in the Chern-Simons formulation of (2 + 1)-dimensional gravity

    International Nuclear Information System (INIS)

    Meusburger, C; Schroers, B J

    2003-01-01

    In the formulation of (2 + 1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincare group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincare transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms

  7. In pursuit of the rhabdophane crystal structure: from the hydrated monoclinic LnPO{sub 4}.0.667H{sub 2}O to the hexagonal LnPO{sub 4} (Ln = Nd, Sm, Gd, Eu and Dy)

    Energy Technology Data Exchange (ETDEWEB)

    Mesbah, Adel, E-mail: adel.mesbah@cea.fr [ICSM, UMR 5257 CNRS – CEA – ENSCM – Université de Montpellier, Site de Marcoule - Bât 426, BP 17171, 30207 Bagnols/Cèze (France); Clavier, Nicolas [ICSM, UMR 5257 CNRS – CEA – ENSCM – Université de Montpellier, Site de Marcoule - Bât 426, BP 17171, 30207 Bagnols/Cèze (France); Elkaim, Erik [Synchrotron SOLEIL, L' Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex (France); Szenknect, Stéphanie; Dacheux, Nicolas [ICSM, UMR 5257 CNRS – CEA – ENSCM – Université de Montpellier, Site de Marcoule - Bât 426, BP 17171, 30207 Bagnols/Cèze (France)

    2017-05-15

    The dehydration process of the hydrated rhabdophane LnPO{sub 4}.0.667H{sub 2}O (Ln = La to Dy) was thoroughly studied over the combination of in situ high resolution synchrotron powder diffraction and TGA experiments. In the case of SmPO{sub 4}.0.667H{sub 2}O (monoclinic, C2), a first dehydration step was identified around 80 °C leading to the formation of SmPO{sub 4}.0.5H{sub 2}O (Monoclinic, C2) with Z =12 and a =17.6264(1) Å, b =6.9704(1) Å, c =12.1141(1) Å, β=133.74(1) °, V =1075.33(1) Å{sup 3}. In agreement with the TGA and dilatometry experiments, all the water molecules were evacuated above 220 °C yielding to the anhydrous form, which crystallizes in the hexagonal P3{sub 1}21 space group with a =7.0389(1) Å, c =6.3702(1) Å and V =273.34(1) Å{sup 3}. This study was extended to selected LnPO{sub 4}.0.667H{sub 2}O samples (Ln= Nd, Gd, Eu, Dy) and the obtained results confirmed the existence of two dehydration steps before the stabilization of the anhydrous form, with the transitory formation of LnPO{sub 4}.0.5H{sub 2}O. - Graphical abstract: The dehydration process of the rhabdophane SmPO{sub 4}.0.667H{sub 2}O was studied over combination of in situ high resolution synchrotron powder diffraction and TGA techniques, a first dehydration was identified around 80 °C leading to the formation of SmPO{sub 4}.0.5H{sub 2}O (Monoclinic, C2). Then above 220 °C, the anhydrous form of the rhabdophane SmPO{sub 4} was stabilized and crystallizes in the hexagonal P3{sub 1}21 space group. - Highlights: • In situ synchrotron powder diffraction was carried out during the dehydration of the rhabdopahe LnPO{sub 4}.0.667H{sub 2}O. • The heat of the rhabdophane LnPO{sub 4}.0.667H{sub 2}O leads to LnPO{sub 4}.0.5H{sub 2}O then to anhydrous rhabdophane LnPO{sub 4}. • LnPO{sub 4}.0.5H{sub 2}O (monoclinic, C2) and LnPO{sub 4} (Hexagonal, P3{sub 1}21) were solved over the use of direct methods.

  8. Inverse semigroups the theory of partial symmetries

    CERN Document Server

    Lawson, Mark V

    1998-01-01

    Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.

  9. A search for symmetries in the genetic code

    International Nuclear Information System (INIS)

    Hornos, J.E.M.; Hornos, Y.M.M.

    1991-01-01

    A search for symmetries based on the classification theorem of Cartan for the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group cannot be found to reproduce the present, universal code. However a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken. (author). 27 refs, 3 figs, 6 tabs

  10. de Sitter symmetry of Neveu-Schwarz spinors

    International Nuclear Information System (INIS)

    Epstein, Henri; Moschella, Ugo

    2016-01-01

    We study the relations between Dirac fields living on the 2-dimensional Lorentzian cylinder and the ones living on the double-covering of the 2-dimensional de Sitter manifold, here identified as a certain coset space of the group SL(2,R). We show that there is an extended notion of de Sitter covariance only for Dirac fields having the Neveu-Schwarz anti-periodicity and construct the relevant cocycle. Finally, we show that the de Sitter symmetry is naturally inherited by the Neveu-Schwarz massless Dirac field on the cylinder.

  11. Critical Role of Monoclinic Polarization Rotation in High-Performance Perovskite Piezoelectric Materials.

    Science.gov (United States)

    Liu, Hui; Chen, Jun; Fan, Longlong; Ren, Yang; Pan, Zhao; Lalitha, K V; Rödel, Jürgen; Xing, Xianran

    2017-07-07

    High-performance piezoelectric materials constantly attract interest for both technological applications and fundamental research. The understanding of the origin of the high-performance piezoelectric property remains a challenge mainly due to the lack of direct experimental evidence. We perform in situ high-energy x-ray diffraction combined with 2D geometry scattering technology to reveal the underlying mechanism for the perovskite-type lead-based high-performance piezoelectric materials. The direct structural evidence reveals that the electric-field-driven continuous polarization rotation within the monoclinic plane plays a critical role to achieve the giant piezoelectric response. An intrinsic relationship between the crystal structure and piezoelectric performance in perovskite ferroelectrics has been established: A strong tendency of electric-field-driven polarization rotation generates peak piezoelectric performance and vice versa. Furthermore, the monoclinic M_{A} structure is the key feature to superior piezoelectric properties as compared to other structures such as monoclinic M_{B}, rhombohedral, and tetragonal. A high piezoelectric response originates from intrinsic lattice strain, but little from extrinsic domain switching. The present results will facilitate designing high-performance perovskite piezoelectric materials by enhancing the intrinsic lattice contribution with easy and continuous polarization rotation.

  12. Monoclinic mixed crystals of halogenomethanes CBr4-nCln (n = 0, ..., 4)

    International Nuclear Information System (INIS)

    Negrier, Philippe; Tamarit, Josep Ll.; Barrio, Maria; Pardo, Luis C.; Mondieig, Denise

    2007-01-01

    On the basis of the isostructural relationship between the low-temperature monoclinic (C2/c, Z = 32) phases of the halogenomethane CBr 4-n Cl n (n = 0, ..., 4), a set of mixed crystals has been analysed by means of high-resolution X-ray powder diffraction. It is shown that the monoclinic structure of pure and mixed crystals does not depend of the particularities of the dipolar (or dipole induced) interactions of the pure compound, neither on the composition of the mixed crystal, but on the relative content of the halogen atoms which controls the size of the molecule or the average molecule for the case of mixed crystals

  13. Nonlinear (super)symmetries and amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Kallosh, Renata [Physics Department, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)

    2017-03-07

    There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E{sub 7(7)} scalar sector symmetries as well as the fermionic goldstino symmetries. We present a universal derivation of the vanishing amplitudes in the single (bosonic or fermionic) soft limit. We explain why, universally, the double-soft limit probes the coset space algebra. We also provide identities describing the multiple-soft limit. We discuss loop corrections to N≥5 supergravity, to the D3 brane, and the UV completion of constrained multiplets in string theory.

  14. Infinite additional symmetries in two-dimensional conformal quantum field theory

    International Nuclear Information System (INIS)

    Zamolodchikov, A.B.

    1986-01-01

    This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form associative algebras with quadratic determining relations. ''Minimal models'' of conforma field theory with such additional symmetries are considered. The space of local fields occurring in a conformal field theory with additional symmetry corresponds to a certain (in general, reducible) representation of the corresponding algebra of the symmetry

  15. NOTE: Circular symmetry in topologically massive gravity

    Science.gov (United States)

    Deser, S.; Franklin, J.

    2010-05-01

    We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.

  16. Towards a Complete Classification of Symmetry-Protected Topological Phases for Interacting Fermions in Three Dimensions and a General Group Supercohomology Theory

    Science.gov (United States)

    Wang, Qing-Rui; Gu, Zheng-Cheng

    2018-01-01

    The classification and construction of symmetry-protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that (generalized) group cohomology theory or cobordism theory gives rise to a complete classification of SPT phases in interacting boson or spin systems. The construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in three dimensions. In this work, we revisit this problem based on an equivalence class of fermionic symmetric local unitary transformations. We construct very general fixed-point SPT wave functions for interacting fermion systems. We naturally reproduce the partial classifications given by special group supercohomology theory, and we show that with an additional B ˜H2(Gb,Z2) structure [the so-called obstruction-free subgroup of H2(Gb,Z2) ], a complete classification of SPT phases for three-dimensional interacting fermion systems with a total symmetry group Gf=Gb×Z2f can be obtained for unitary symmetry group Gb. We also discuss the procedure for deriving a general group supercohomology theory in arbitrary dimensions.

  17. Automorphic Lie algebras with dihedral symmetry

    International Nuclear Information System (INIS)

    Knibbeler, V; Lombardo, S; A Sanders, J

    2014-01-01

    The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl 2 (C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits. (paper)

  18. An introduction to Yangian symmetries

    International Nuclear Information System (INIS)

    Bernard, D.

    1992-01-01

    Some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories are reviewed. They include two main issues: the first is the classical Heisenberg model, covering non-Abelian symmetries, generators of the symmetries and the semi-classical Yangians, an alternative presentation of the semi-classical Yangians, digression on Poisson-Lie groups. The second is the quantum Heisenberg chain, covering non-Abelian symmetries and the quantum Yangians, the transfer matrix and an alternative presentation of the Yangians, digression on the double Yangians. (K.A.) 15 refs

  19. Structural, mechanical, and electronic properties of monoclinic N{sub 2}H{sub 5}N{sub 3} under pressure

    Energy Technology Data Exchange (ETDEWEB)

    Qi-Jun, Liu; Fu-Sheng, Liu, E-mail: qijunliu@home.swjtu.edu.cn [School of Physical Science and Technology, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu (China); Bond and Band Engineering Group, Sichuan Provincial Key Laboratory (for Universities) of High Pressure Science and Technology, Southwest Jiaotong University, Chengdu (China); Zheng-Tang, Liu [State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi' an, (China)

    2015-08-15

    Structural, elastic, mechanical, and electronic properties of monoclinic N{sub 2}H{sub 5}N{sub 3} at zero and high pressure have been investigated using the plane-wave ultrasoft pseudopotential method within the density-functional theory (DFT). The pressure dependences of structural parameters, elastic constants, mechanical properties, band gaps, and density of states of monoclinic N{sub 2}H{sub 5}N{sub 3} have been calculated and discussed. The obtained results show that monoclinic N{sub 2}H{sub 5}N{sub 3} is unstable at pressures exceeding the value 126.1 GPa. The ratio of B/G and the Cauchy’s pressure indicate that monoclinic N{sub 2}H{sub 5}N{sub 3} behaves in ductile nature with pressure ranging from 0 to 200 GPa. (author)

  20. Extended Galilean symmetries of non-relativistic strings

    Energy Technology Data Exchange (ETDEWEB)

    Batlle, Carles [Departament de Matemàtiques and IOC, Universitat Politècnica de Catalunya, EPSEVG,Av. V. Balaguer 1, E-08808 Vilanova i la Geltrú (Spain); Gomis, Joaquim; Not, Daniel [Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB),Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain)

    2017-02-09

    We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.

  1. Monoclinic phase transformation and mechanical durability of zirconia ceramic after fatigue and autoclave aging.

    Science.gov (United States)

    Mota, Yasmine A; Cotes, Caroline; Carvalho, Rodrigo F; Machado, João P B; Leite, Fabíola P P; Souza, Rodrigo O A; Özcan, Mutlu

    2017-10-01

    This study evaluated the influence of two aging procedures on the biaxial flexural strength of yttria-stabilized tetragonal zirconia ceramics. Disc-shaped zirconia specimens and (ZE: E.max ZirCAD, Ivoclar; ZT: Zirkon Translucent, Zirkonzahn) (N = 80) (∅:12 mm; thickness:1.2 mm, ISO 6872) were prepared and randomly divided into four groups (n = 10 per group) according to the aging procedures: C: Control, no aging; M: mechanical cycling (2 × 10 6 cycles/3.8 Hz/200 N); AUT: Aging in autoclave at 134°C, 2 bar for 24 h; AUT + M: Autoclave aging followed by mechanical cycling. After aging, the transformed monoclinic zirconia (%) were evaluated using X-ray diffraction and surface roughness was measured using atomic force microscopy. The average grain size was measured by scanning electron microscopy and the specimens were submitted to biaxial flexural strength testing (1 mm/min, 1000 kgf in water). Data (MPa) were statistically analyzed using 2-way analysis of variance and Tukey's test (α = 0.05). Aging procedures significantly affected (p = 0.000) the flexural strength data but the effect of zirconia type was not significant (p = 0.657). AUT ZT (936.4 ± 120.9 b ) and AUT + M ZE (867.2 ± 49.3 b ) groups presented significantly higher values (p autoclave aging alone or with mechanical aging increased the flexure strength but also induced higher transformation from tetragonal to monoclinic phase in both zirconia materials tested. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 1972-1977, 2017. © 2016 Wiley Periodicals, Inc.

  2. From Quantum Deformations of Relativistic Symmetries to Modified Kinematics and Dynamics

    International Nuclear Information System (INIS)

    Lukierski, J.

    2010-01-01

    We present a short review describing the use of noncommutative spacetime in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their realizations (noncommutative modules) as important mathematical tool describing quantum-deformed symmetries: quantum Lie groups and quantum Lie algebras. We consider in some detail the most studied examples of noncommutative space-time geometry: the canonical and κ-deformed cases. Finally, we briefly describe the modifications of Einstein gravity obtained by introduction of noncommutative space-time coordinates. (author)

  3. Symmetry of quantum intramolecular dynamics

    International Nuclear Information System (INIS)

    Burenin, Alexander V

    2002-01-01

    The paper reviews the current progress in describing quantum intramolecular dynamics using merely symmetry principles as a basis. This closed qualitative approach is of particular interest because it is the only method currently available for a broad class of topical problems in the internal dynamics of molecules. Moreover, a molecule makes a physical system whose collective internal motions are geometrically structured, so that its description by perturbation methods requires a symmetry analysis of this structure. The nature of the geometrical symmetry groups crucial for the closed formulation of the qualitative approach is discussed. In particular, the point group of a molecule is of this type. (methodological notes)

  4. Symmetry and symmetry breaking in modern physics

    International Nuclear Information System (INIS)

    Barone, M; Theophilou, A K

    2008-01-01

    In modern physics, the theory of symmetry, i.e. group theory, is a basic tool for understanding and formulating the fundamental principles of Physics, like Relativity, Quantum Mechanics and Particle Physics. In this work we focus on the relation between Mathematics, Physics and objective reality

  5. Anisotropic crystal structure distortion of the monoclinic polymorph of acetaminophen at high hydrostatic pressures.

    Science.gov (United States)

    Boldyreva, E V; Shakhtshneider, T P; Vasilchenko, M A; Ahsbahs, H; Uchtmann, H

    2000-04-01

    The anisotropy of structural distortion of the monoclinic polymorph of acetaminophen induced by hydrostatic pressure up to 4.0 GPa was studied by single-crystal X-ray diffraction in a Merrill-Bassett diamond anvil cell (DAC). The space group (P2(1)/n) and the general structural pattern remained unchanged with pressure. Despite the overall decrease in the molar volume with pressure, the structure expanded in particular crystallographic directions. One of the linear cell parameters (c) passed through a minimum as the pressure increased. The intramolecular bond lengths changed only slightly with pressure, but the changes in the dihedral and torsion angles were very large. The compressibility of the intermolecular hydrogen bonds NH...O and OH...O was measured. NH...O bonds were shown to be slightly more compressible than OH...O bonds. The anisotropy of structural distortion was analysed in detail in relation to the pressure-induced changes in the molecular conformations, to the compression of the hydrogen-bond network, and to the changes in the orientation of molecules with respect to each other in the pleated sheets in the structure. Dirichlet domains were calculated in order to analyse the relative shifts of the centroids of the hydrogen-bonded cycles and of the centroids of the benzene rings with pressure.

  6. Symmetry of crystals and molecules

    CERN Document Server

    Ladd, Mark

    2014-01-01

    This book successfully combines a thorough treatment of molecular and crystalline symmetry with a simple and informal writing style. By means of familiar examples the author helps to provide the reader with those conceptual tools necessary for the development of a clear understanding of what are often regarded as 'difficult' topics. Christopher Hammond, University of Leeds This book should tell you everything you need to know about crystal and molecular symmetry. Ladd adopts an integrated approach so that the relationships between crystal symmetry, molecular symmetry and features of chemical interest are maintained and reinforced. The theoretical aspects of bonding and symmetry are also well represented, as are symmetry-dependent physical properties and the applications of group theory. The comprehensive coverage will make this book a valuable resource for a broad range of readers.

  7. Symmetries of collective models in intrinsic frame

    International Nuclear Information System (INIS)

    Gozdz, A.; Pedrak, A.; Szulerecka, A.; Dobrowolski, A.; Dudek, J.

    2013-01-01

    In the paper a very general definition of intrinsic frame, by means of group theoretical methods, is introduced. It allows to analyze nuclear properties which are invariant in respect to the group which defines the intrinsic frame. For example, nuclear shape is a well determined feature in the intrinsic frame defined by the Euclidean group. It is shown that using of intrinsic frame gives an opportunity to consider intrinsic nuclear symmetries which are independent of symmetries observed in the laboratory frame. An importance of the notion of partial symmetries is emphasized. (author)

  8. Quantum mechanics and hidden superconformal symmetry

    Science.gov (United States)

    Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

    2017-12-01

    Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

  9. Additional symmetries of supersymmetric KP hierarchies

    International Nuclear Information System (INIS)

    Stanciu, S.

    1993-09-01

    We investigate the additional symmetries of several supersymmetric KP hierarchies: The SKP hierarchy of Manin and Radul, the SKP 2 hierarchy, and the Jacobian SKP hierarchy. The main technical tool is the supersymmetric generalisation of a map originally due to Radul between the Lie algebra of superdifferential operators and the Lie algebra of vector fields on the space of supersymmetric Lax operators. In the case of the Manin-Radul SKP hierarchy we identify additional symmetries which form an algebra isomorphic to a subalgebra of superdifferential operators; whereas in the case of the Jacobian SKP, the (additional) symmetries are identified with the algebra itself. (orig.)

  10. Entanglement entropy and nonabelian gauge symmetry

    International Nuclear Information System (INIS)

    Donnelly, William

    2014-01-01

    Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang–Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity. (paper)

  11. Group Theory of Wannier Functions Providing the Basis for a Deeper Understanding of Magnetism and Superconductivity

    Directory of Open Access Journals (Sweden)

    Ekkehard Krüger

    2015-05-01

    Full Text Available The paper presents the group theory of optimally-localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all of the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into optimally-localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M or to a subgroup of G or M. In this context, the paper considers usual, as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors (Ekkehard Krüger in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the optimally-localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly-correlated localized electrons makes clear predictions of whether or not the system can possess superconducting or magnetic eigenstates.

  12. Structures of ordered tungsten- or molybdenum-containing quaternary perovskite oxides

    International Nuclear Information System (INIS)

    Day, Bradley E.; Bley, Nicholas D.; Jones, Heather R.; McCullough, Ryan M.; Eng, Hank W.; Porter, Spencer H.; Woodward, Patrick M.; Barnes, Paris W.

    2012-01-01

    The room temperature crystal structures of six A 2 MMoO 6 and A 2 MWO 6 ordered double perovskites were determined from X-ray and neutron powder diffraction data. Ba 2 MgWO 6 and Ba 2 CaMoO 6 both adopt cubic symmetry (space group Fm3-bar m, tilt system a 0 a 0 a 0 ). Ba 2 CaWO 6 has nearly the same tolerance factor (t=0.972) as Ba 2 CaMoO 6 (t=0.974), yet it surprisingly crystallizes with I4/m symmetry indicative of out-of-phase rotations of the MO 6 octahedra about the c-axis (a 0 a 0 c − ). Sr 2 ZnMoO 6 (t=0.979) also adopts I4/m symmetry; whereas, Sr 2 ZnWO 6 (t=0.976) crystallizes with monoclinic symmetry (P2 1 /n) with out-of-phase octahedral tilting distortions about the a- and b-axes, and in-phase tilting about the c-axis (a − a − c + ). Ca 2 CaWO 6 (t=0.867) also has P2 1 /n symmetry with large tilting distortions about all three crystallographic axes and distorted CaO 6 octahedra. Analysis of 93 double perovskites and their crystal structures showed that while the type and magnitude of the octahedral tilting distortions are controlled primarily by the tolerance factor, the identity of the A-cation acts as the secondary structure directing factor. When A=Ba 2+ the boundary between cubic and tetragonal symmetries falls near t=0.97, whereas when A=Sr 2+ this boundary falls somewhere between t=1.018 and t=0.992. - Graphical abstract: A survey of the tolerance factor of 41 Mo/W- and 52 Nb/Ta-containing quaternary perovskites plotted as a function of the difference between the two six-coordinate M-cation ionic radii. Compounds with cubic symmetry are represented by diamonds, those with tetragonal symmetry are represented by squares, those with I2/m monoclinic symmetry are represented by ×, and those with P2 1 /n monoclinic symmetry are represented by triangles. White symbols represent compositions where A=Ba 2+ , gray symbols represent compositions where A=Sr 2+ , and black symbols represent where A=Ca 2+ . The filled circle represents rhombohedral Ba 2

  13. 2-surface twistors, embeddings and symmetries

    International Nuclear Information System (INIS)

    Jeffryes, B.P.

    1987-01-01

    2-Surface twistor space was introduced in connection with a proposal for a quasi-local definition of mass and angular momentum within general relativity. Properties of the 2-surface twistor space are related to the possibilities for embedding the 2-surface in real and complex conformally flat spaces. The additional properties of the twistor space resulting from symmetries of the 2-surface are discussed, with particular detail on axisymmetric 2-surfaces. (author)

  14. Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry

    Directory of Open Access Journals (Sweden)

    Chikashi Arita

    2012-10-01

    Full Text Available We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement entropies from the double scaling limit. We also evaluate the geometric entanglement, which serves as another measure for entanglement. We find the geometric entanglement reaches its maximum at the isotropic point, and decreases with the increase of the anisotropy. This behavior is similar to that of the entanglement entropies.

  15. Group-invariant finite Fourier transforms

    International Nuclear Information System (INIS)

    Shenefelt, M.H.

    1988-01-01

    The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

  16. Mapping spaces and automorphism groups of toric noncommutative spaces

    Science.gov (United States)

    Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.

    2017-09-01

    We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application, we study the `internalized' automorphism group of a toric noncommutative space and show that its Lie algebra has an elementary description in terms of braided derivations.

  17. Crystallographic characterization and molecular symmetry of edestin, a legumin from hemp.

    Science.gov (United States)

    Patel, S; Cudney, R; McPherson, A

    1994-01-07

    Edestin, a legumin class reserve protein from hemp seeds having six identical subunits was crystallized from ammonium phosphate at pH 5 and subsequently characterized by X-ray diffraction. The crystals are of space group R32 with a = 127 A and gamma = 116 degrees having an equivalent triply centered hexagonal cell of a = b = 215 A, c = 80 A. There is one hexameric protein in the rhombohedral unit cell, hence the subunits of the Edestin molecule must be arranged with 32 point group symmetry.

  18. Nonlinear realizations of W3 symmetry

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Krivonos, S.O.

    1991-01-01

    We derive the Toda lattice realization of classical W 3 symmetry on two scalar fields in a purely geometric way, proceeding from a nonlinear realization of some associate higher-spin symmetry W 3 ∞ is derived. The Toda lattice equations are interpreted as the constraints singling out a two-dimensional fully geodesic subspace in the initial coset space of W 3 ∞ . This subspace is the quotient of SL(3,R) over its maximal parabolic subgroup. 20 refs

  19. The zonal satellite problem. III Symmetries

    Directory of Open Access Journals (Sweden)

    Mioc V.

    2002-01-01

    Full Text Available The two-body problem associated with a force field described by a potential of the form U =Sum(k=1,n ak/rk (r = distance between particles, ak = real parameters is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita’s coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure.

  20. Anomalous Symmetry Fractionalization and Surface Topological Order

    Directory of Open Access Journals (Sweden)

    Xie Chen

    2015-10-01

    Full Text Available In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain “anomalous” SETs can only occur on the surface of a 3D symmetry-protected topological (SPT phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H^{4}(G,U(1, which also precisely labels the set of 3D SPT phases, with symmetry group G. An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U(1_{2}] topological order with a reduced symmetry Z_{2}×Z_{2}⊂SO(3, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.

  1. General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

    International Nuclear Information System (INIS)

    Reshetnyak, A.

    2013-01-01

    We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST–BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, (arXiv:1110.5044 [hep-th])]. Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to osp(k|2k) superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spin-tensor field of spin (5/2,3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2,3/2)

  2. Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies

    International Nuclear Information System (INIS)

    Elokaby, Ayman

    2009-01-01

    The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the crossing number 7 plays the role of threshold similar to 4 and 5 in E-infinity theory and for the 11 crossing the number of distinct knots is very close to 4α-bar 0 +1=548+1=549, where α-bar 0 =137 is the inverse integer electromagnetic fine structure constant. This is particularly intriguing in view of a similar relation pertinent to the 17 two and three Stein spaces where the total dimension is Σ 1 17 Stein=5α-bar 0 +1=685+1=686, as well as the sum of the eight exceptional Lie symmetry groups Σ i=1 8 |E i |=4α-bar 0 =548. The slight discrepancy of one is explained in both cases by the inclusion of El Naschie's transfinite corrections leading to Σ i=1 8 |E i |=(4)(137+k 0 )=548.328157 and Σ i=1 17 Stein=(5)(137+k 0 )=685.41097, where k o = φ 5 (1 - φ 5 ) and φ=(√(5)-1)/2.

  3. Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

    Directory of Open Access Journals (Sweden)

    Hongwei Yang

    2012-01-01

    Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

  4. Symmetries and conserved quantities in geodesic motion

    International Nuclear Information System (INIS)

    Hojman, S.; Nunez, L.; Patino, A.; Rago, H.

    1986-01-01

    Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved

  5. N=1 superstrings with spontaneously broken symmetries

    International Nuclear Information System (INIS)

    Ferrara, S.

    1988-01-01

    We construct N=1 chiral superstrings with spontaneously broken gauge symmetry in four space-time dimensions. These new string solutions are obtained by a generalized coordinate-dependent Z 2 orbifold compactification of some non-chiral five-dimensional N=1 and N=2 superstrings. The scale of symmetry breaking is arbitrary (at least classically) and it can be chosen hierarchically smaller than the string scale (α') -1/2 . (orig.)

  6. Spinors and supersymmetry in four-dimensional Euclidean space

    International Nuclear Information System (INIS)

    McKeon, D.G.C.; Sherry, T.N.

    2001-01-01

    Spinors in four-dimensional Euclidean space are treated using the decomposition of the Euclidean space SO(4) symmetry group into SU(2)xSU(2). Both 2- and 4-spinor representations of this SO(4) symmetry group are shown to differ significantly from the corresponding spinor representations of the SO(3, 1) symmetry group in Minkowski space. The simplest self conjugate supersymmetry algebra allowed in four-dimensional Euclidean space is demonstrated to be an N=2 supersymmetry algebra which resembles the N=2 supersymmetry algebra in four-dimensional Minkowski space. The differences between the two supersymmetry algebras gives rise to different representations; in particular an analysis of the Clifford algebra structure shows that the momentum invariant is bounded above by the central charges in 4dE, while in 4dM the central charges bound the momentum invariant from below. Dimensional reduction of the N=1 SUSY algebra in six-dimensional Minkowski space (6dM) to 4dE reproduces our SUSY algebra in 4dE. This dimensional reduction can be used to introduce additional generators into the SUSY algebra in 4dE. Well known interpolating maps are used to relate the N=2 SUSY algebra in 4dE derived in this paper to the N=2 SUSY algebra in 4dM. The nature of the spinors in 4dE allows us to write an axially gauge invariant model which is shown to be both Hermitian and anomaly-free. No equivalent model exists in 4dM. Useful formulae in 4dE are collected together in two appendixes

  7. Carbonyltrichlorotris(dimethylphenylphosphine)technetium-ethanol (1/1), the first seven-coordinate complex of technetium; position of this molecule in the Csub(3v) family

    Energy Technology Data Exchange (ETDEWEB)

    Bandoli, G; Clemente, D A; Mazzi, U [Consiglio Nazionale delle Ricerche, Padua (Italy). Lab. di Chimica e Tecnologia dei Radioelementi

    1978-01-01

    The preparation and the crystal and molecular structure of the title complex are reported. The coordination polyhedron is that of a distorted capped octahedron Csub(3v) symmetry). The technetium atom is seven-coordnate and bonded to three phosphine ligands (capped face), three chlorine ligands (uncapped face), and to the carbonyl group, which occupies the unique capping position. Crystals are monoclinic, space group P2/sub 1//c, with cell dimensions a = 11.732(9), b = 11.807(9), c = 23.588(12) A, and ..beta..103.42(8)/sup 0/. The structure has been refined by least squares to a conventional R of 0.093 for 1 794 observed reflections. Metal-ligand bond lengths are: Tc-CO 1.86(2), Tc-C1 2.48(1). and Tc-p 2.44(1) A. Seven coordinate complexes are briefly reviewed: in particular, a description of Csub(3v) symmetry and its distortions has been developed in terms of repulsion theory and the angular-overlap model.

  8. Space, time and conservation laws

    International Nuclear Information System (INIS)

    Aronov, R.A.; Ugarov, V.A.

    1978-01-01

    The Neter theorem establishing correspondence between conservation laws and symmetry properties (space and time in particular) is considered. The theorem is based on one of the possible ways of finding equations of motion for a physical system. From a certain expression (action functional) equations of motion for a system can be obtained which do not contain new physical assertions in principal in comparison with the Newtonian laws. Neter suggested a way of deriving conservation laws by transforming space and time coordinates. Neter theorem consequences raise a number of problems: 1). Are conservation laws (energy, momentum) consequences of space and time symmetry properties. 2). Is it possible to obtain conservation laws in theory neglecting equations of motion. 3). What is of the primary importance: equations of motion, conservation laws or properties of space and time symmetry. It is shown that direct Neter theorem does not testify to stipulation of conservation laws by properties of space and time symmetry and symmetry properties of other non-space -time properties of material systems in objective reality. It says nothing of whether there is any subordination between symmetry properties and conservation laws

  9. Dynamics symmetries of Hamiltonian system on time scales

    Energy Technology Data Exchange (ETDEWEB)

    Peng, Keke, E-mail: pengkeke88@126.com; Luo, Yiping, E-mail: zjstulyp@126.com [Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)

    2014-04-15

    In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.

  10. Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations

    KAUST Repository

    Alghamdi, Moataz

    2017-06-18

    We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.

  11. Family symmetries in F-theory GUTs

    CERN Document Server

    King, S F; Ross, G G

    2010-01-01

    We discuss F-theory SU(5) GUTs in which some or all of the quark and lepton families are assigned to different curves and family symmetry enforces a leading order rank one structure of the Yukawa matrices. We consider two possibilities for the suppression of baryon and lepton number violation. The first is based on Flipped SU(5) with gauge group SU(5)\\times U(1)_\\chi \\times SU(4)_{\\perp} in which U(1)_{\\chi} plays the role of a generalised matter parity. We present an example which, after imposing a Z_2 monodromy, has a U(1)_{\\perp}^2 family symmetry. Even in the absence of flux, spontaneous breaking of the family symmetry leads to viable quark, charged lepton and neutrino masses and mixing. The second possibility has an R-parity associated with the symmetry of the underlying compactification manifold and the flux. We construct an example of a model with viable masses and mixing angles based on the gauge group SU(5)\\times SU(5)_{\\perp} with a U(1)_{\\perp}^3 family symmetry after imposing a Z_2 monodromy.

  12. Pressure-induced phase transformation of HfO2

    International Nuclear Information System (INIS)

    Arashi, H.

    1992-01-01

    This paper reports on the pressure dependence of the Raman spectra of HfO 2 that was measured by a micro-Raman technique using a single-crystal specimen in the pressure range from 0 to 10 GPa at room temperature. The symmetry assignment of Raman bands of the monoclinic phase was experimentally accomplished from the polarization measurements for the single crystal. With increased pressure, a phase transformation for the monoclinic phase took place at 4.3 ± 0.3 GPa. Nineteen Raman bands were observed for the high-pressure phase. The spectral structure of the Raman bands for the high-pressure phase was similar with those reported previously for ZrO 2 . The space group for the high pressure phase of HfO 2 was determined as Pbcm, which was the same as that of the high-pressure phase for ZrO 2 on the basis of the number and the spectral structure of the Raman bands

  13. Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface

    Directory of Open Access Journals (Sweden)

    Meng Cheng

    2016-12-01

    Full Text Available The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a “spinon” excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of “anyonic spin-orbit coupling,” which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.

  14. Landau-Ginzburg orbifolds and symmetries of K3 CFTs

    International Nuclear Information System (INIS)

    Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; Paquette, Natalie M.

    2017-01-01

    Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K 3 string theory. To test and clarify these proposed K 3 -moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K 3 sigma models. We compute K 3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M 11 c 2.M 12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Finally, our results provide strong evidence for the relevance of umbral moonshine for K 3 symmetries, as well as new hints for its eventual explanation.

  15. Novel S = 1/2 Kagome Lattice Materials: Cs2TiCu3F12 and Rb2TiCu3F12

    Directory of Open Access Journals (Sweden)

    Lewis J. Downie

    2015-05-01

    Full Text Available Two new members of the A2B′Cu3F12 family of kagome-related materials have been prepared, in order to further understand the crystal-chemical relationships, phase transitions and magnetic behaviour within this family of potentially frustrated S = ½ two-dimensional quantum magnets. Cs2TiCu3F12 adopts a crystal structure with the ideal kagome lattice topology (space group R m at ambient temperature. Diffraction studies reveal different symmetry-lowering structural phase transitions in single crystal and polycrystalline forms at sub-ambient temperatures, with the single crystal form retaining rhombohedral symmetry and the powder form being monoclinic. In both cases, long-range antiferromagnetic order occurs in the region 16–20 K. Rb2TiCu3F12 adopts a distorted triclinic structure even at ambient temperatures.

  16. Calculation of magnetization curves and probability distribution for monoclinic and uniaxial systems

    International Nuclear Information System (INIS)

    Sobh, Hala A.; Aly, Samy H.; Yehia, Sherif

    2013-01-01

    We present the application of a simple classical statistical mechanics-based model to selected monoclinic and hexagonal model systems. In this model, we treat the magnetization as a classical vector whose angular orientation is dictated by the laws of equilibrium classical statistical mechanics. We calculate for these anisotropic systems, the magnetization curves, energy landscapes and probability distribution for different sets of relevant parameters and magnetic fields of different strengths and directions. Our results demonstrate a correlation between the most probable orientation of the magnetization vector, the system's parameters, and the external magnetic field. -- Highlights: ► We calculate magnetization curves and probability angular distribution of the magnetization. ► The magnetization curves are consistent with probability results for the studied systems. ► Monoclinic and hexagonal systems behave differently due to their different anisotropies

  17. Constraining the physical state by symmetries

    Science.gov (United States)

    Fatibene, L.; Ferraris, M.; Magnano, G.

    2017-03-01

    After reviewing the hole argument and its relations with initial value problem and general covariance, we shall discuss how much freedom one has to define the physical state in a generally covariant field theory (with or without internal gauge symmetries). Our analysis relies on Cauchy problems, thus it is restricted to globally hyperbolic spacetimes. We shall show that in generally covariant theories on a compact space (as well as for internal gauge symmetries on any spacetime) one has no freedom and one is forced to declare as physically equivalent two configurations which differ by a global spacetime diffeomorphism (or by an internal gauge transformation) as it is usually prescribed. On the contrary, when space is not compact, the result does not hold true and one may have different options to define physically equivalent configurations, still preserving determinism. For this scenario to be effective, the group G of formal transformations needs to be a subgroup of dynamical symmetries (otherwise field equations, which are written in terms of configurations would not induce equations for the physical state classes) and it must contain the group D generated by Cauchy transformations (otherwise the equations induced on physical state classes would not be well posed, either). We argue that it is exactly because of this double inclusion that the hole argument in its initial problem formulation is more powerful than in its boundary formulation. In the boundary formulation of the hole argument one still has that the group G of formal transformations is a subgroup of dynamical symmetries, but there is no evidence for it to contain a particular non-trivial subgroup.In this paper we shall show that this scenario is exactly implemented in generally covariant theories. In the last section we shall show it to be implemented in gauge theories as well.Norton also argued (see [1]) that the definition of physical state is something to be discussed in physics and it is not

  18. Hypersurfaces in Pn with 1-parameter symmetry groups II

    DEFF Research Database (Denmark)

    Plessis, Andrew du; Wall, C.T.C.

    2010-01-01

    We assume V a hypersurface of degree d in with isolated singularities and not a cone, admitting a group G of linear symmetries. In earlier work we treated the case when G is semi-simple; here we analyse the unipotent case. Our first main result lists the possible groups G. In each case we discuss...... the geometry of the action, reduce V to a normal form, find the singular points, study their nature, and calculate the Milnor numbers. The Tjurina number τ(V) ≤ (d − 1) n–2(d 2 − 3d + 3): we call V oversymmetric if this value is attained. We calculate τ in many cases, and characterise the oversymmetric...

  19. The monoclinic superstructure of the M{sub 2}Pt{sub 6}Al{sub 15} series (M=Ca, Sc, Y, La, Lu)

    Energy Technology Data Exchange (ETDEWEB)

    Radzieowski, Mathis; Stegemann, Frank; Hoffmann, Rolf-Dieter [Muenster Univ. (Germany). Inst. fuer Anorganische und Analytische Chemie; Janka, Oliver [Muenster Univ. (Germany). Inst. fuer Anorganische und Analytische Chemie; Oldenburg Univ. (Germany). Inst. fuer Chemie

    2017-07-01

    The five ternary intermetallic compounds M{sub 2}Pt{sub 6}Al{sub 15} (M=Ca, Sc, Y, La, Lu) were prepared from the elements by arc-melting. The crystal structure was determined via single crystal X-ray diffraction. The title compounds crystallize in a superstructure of the RE{sub 0.67}Pt{sub 2}Al{sub 5} type structure (P6{sub 3}/mmc) in the monoclinic crystal system with space group P12{sub 1}/m1 (Sc{sub 2}Pt{sub 6}Al{sub 15}: a=734.19(2), b=1628.96(10), c=734.19(2) pm, β=119.999(3) ; wR=0.0356, 3034 F{sup 2} values, 68 variables). The superstructure can be derived by the superspace formalism using (3+2)D or (3+1)D interpretations of the diffraction data. The structural relation to the subcell structure is discussed on the basis of a group-subgroup scheme. In the crystal structure strongly bonded [Pt{sub 2}Al{sub 4}]{sup δ-} slabs are alternatingly stacked with ordered layers containing M atoms and Al{sub 3} triangles.

  20. Quantum group gauge theory on quantum spaces

    International Nuclear Information System (INIS)

    Brzezinski, T.; Majid, S.

    1993-01-01

    We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SU q (2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces). (orig.)

  1. Low energy theorems of hidden local symmetries

    International Nuclear Information System (INIS)

    Harada, Masayasu; Kugo, Taichiro; Yamawaki, Koichi.

    1994-01-01

    We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space G/H, with G and H being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian. (author)

  2. Symmetry of quantum molecular dynamics

    International Nuclear Information System (INIS)

    Burenin, A.V.

    2002-01-01

    The paper reviews the current state-of-art in describing quantum molecular dynamics based on symmetry principles alone. This qualitative approach is of particular interest as the only method currently available for a broad and topical class of problems in the internal dynamics of molecules. Besides, a molecule is a physical system whose collective internal motions are geometrically structured, and its perturbation theory description requires a symmetry analysis of this structure. The nature of the geometrical symmetry groups crucial for the closed formulation of the qualitative approach is discussed [ru

  3. Chiral symmetry and chiral-symmetry breaking

    International Nuclear Information System (INIS)

    Peskin, M.E.

    1982-12-01

    These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed

  4. Peripheral Contour Grouping and Saccade Targeting: The Role of Mirror Symmetry

    Directory of Open Access Journals (Sweden)

    Michaël Sassi

    2014-01-01

    Full Text Available Integrating shape contours in the visual periphery is vital to our ability to locate objects and thus make targeted saccadic eye movements to efficiently explore our surroundings. We tested whether global shape symmetry facilitates peripheral contour integration and saccade targeting in three experiments, in which observers responded to a successful peripheral contour detection by making a saccade towards the target shape. The target contours were horizontally (Experiment 1 or vertically (Experiments 2 and 3 mirror symmetric. Observers responded by making a horizontal (Experiments 1 and 2 or vertical (Experiment 3 eye movement. Based on an analysis of the saccadic latency and accuracy, we conclude that the figure-ground cue of global mirror symmetry in the periphery has little effect on contour integration or on the speed and precision with which saccades are targeted towards objects. The role of mirror symmetry may be more apparent under natural viewing conditions with multiple objects competing for attention, where symmetric regions in the visual field can pre-attentively signal the presence of objects, and thus attract eye movements.

  5. Symmetries of string, M- and F-theories

    NARCIS (Netherlands)

    Bergshoeff, Eric; Proeyen, Antoine Van

    2001-01-01

    The d = 10 type II string theories, d = 11 M-theory and d = 12 F-theory have the same symmetry group. It can be viewed either as a subgroup of a conformal group OSp(1|64) or as a contraction of OSp(1|32). The theories are related by different identifications of their symmetry operators as generators

  6. Symmetry Analysis and Exact Solutions of (2+1)-Dimensional Sawada-Kotera Equation

    International Nuclear Information System (INIS)

    Zhi Hongyan; Zhang Hongqing

    2008-01-01

    Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the (2+1)-dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou's direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko-Dubrovsky equations, respectively.

  7. Dual symmetry in gauge theories

    International Nuclear Information System (INIS)

    Koshkarov, A.L.

    1997-01-01

    Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative interpretation is the quasi-Maxwell linear theory with magnetic charge. Analogous approach is possible in the Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion equations possess the same instanton solutions as the conventional Yang-Mills equations have. An Abelian two-parameter dual group is found to exist in gravitation. Irreducible representations have been obtained: the curvature tensor was expanded into the sum of twice anti-self-dual and self-dual parts. Gravitational instantons are defined as (real )solutions to the usual duality equations. Central symmetry solutions to these equations are obtained. The twice anti-self-dual part of the curvature tensor may be used for introduction of new gravitational equations generalizing Einstein''s equations. However, the theory obtained reduces to the conformal-flat Nordstroem theory

  8. Canadian space agency discipline working group for space dosimetry and radiation science

    International Nuclear Information System (INIS)

    Waker, Anthony; Waller, Edward; Lewis, Brent; Bennett, Leslie; Conroy, Thomas

    2008-01-01

    Full text: One of the great technical challenges in the human and robotic exploration of space is the deleterious effect of radiation on humans and physical systems. The magnitude of this challenge is broadly understood in terms of the sources of radiation, however, a great deal remains to be done in the development of instrumentation, suitable for the space environment, which can provide real-time monitoring of the complex radiation fields encountered in space and a quantitative measure of potential biological risk. In order to meet these research requirements collaboration is needed between experimental nuclear instrumentation scientists, theoretical scientists working on numerical modeling techniques and radiation biologists. Under the auspices of the Canadian Space Agency such a collaborative body has been established as one of a number of Discipline Working Groups. Members of the Space Dosimetry and Radiation Science working group form a collaborative network across Canada including universities, government laboratories and the industrial sector. Three central activities form the core of the Space Dosimetry and Radiation Science DWG. An instrument sub-group is engaged in the development of instruments capable of gamma ray, energetic charged particle and neutron dosimetry including the ability to provide dosimetric information in real-time. A second sub-group is focused on computer modeling of space radiation fields in order to assess the performance of conceptual designs of detectors and dosimeters or the impact of radiation on cellular and sub-cellular biological targets and a third sub-group is engaged in the study of the biological effects of space radiation and the potential of biomarkers as a method of assessing radiation impact on humans. Many working group members are active in more than one sub-group facilitating communication throughout the whole network. A summary progress-report will be given of the activities of the Discipline Working Group and the

  9. Infinite symmetry in the quantum Hall effect

    Directory of Open Access Journals (Sweden)

    Lütken C.A.

    2014-04-01

    Full Text Available The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the symmetry is in increasingly accurate agreement with scaling experiments. The symmetry severely constrains the structure of the effective quantum field theory that encodes the low energy limit of quantum electrodynamics of 1010 charges in two dirty dimensions. If this is a non-linear σ-model the target space is a torus, rather than the more familiar sphere. One of the simplest toroidal models gives a critical (correlation length exponent that agrees with the value obtained from numerical simulations of the quantum Hall effect.

  10. Some general constraints on identical band symmetries

    International Nuclear Information System (INIS)

    Guidry, M.W.; Strayer, M.R.; Wu, C.; Feng, D.H.

    1993-01-01

    We argue on general grounds that nearly identical bands observed for superdeformation and less frequently for normal deformation must be explicable in terms of a symmetry having a microscopic basis. We assume that the unknown symmetry is associated with a Lie algebra generated by terms bilinear in fermion creation and annihilation operators. Observed features of these bands and the general properties of Lie groups are then used to place constraints on acceptable algebras. Additional constraints are placed by assuming that the collective spectrum is associated with a dynamical symmetry, and examining the subgroup structure required by phenomenology. We observe that requisite symmetry cannot be unitary, and that the simplest known group structures consistent with these minimal criteria are associated with the Ginocchio algebras employed in the fermion dynamical symmetry model. However, our arguments are general in nature, and we propose that they imply model-independent constraints on any candidate explanation for identical bands

  11. KINETIC STUDY OF SELECTIVE GAS-PHASE OXIDATION OF ISOPROPANOL TO ACETONE USING MONOCLINIC ZRO2 AS A CATALYST

    Directory of Open Access Journals (Sweden)

    Mohammad Sadiq

    2015-08-01

    Full Text Available Zirconia was prepared by a precipitation method and calcined at 723 K, 1023 K, and 1253 K in order to obtain monoclinic zirconia. The prepared zirconia was characterized by XRD, SEM, EDX, surface area and pore size analyzer, and particle size analyzer. Monoclinic ZrO2 as a catalyst was used for the gas-phase oxidation of isopropanol to acetone in a Pyrex-glass-flow-type reactor with a temperature range of 443 K - 473 K. It was found that monoclinic ZrO2 shows remarkable catalytic activity (68% and selectivity (100% for the oxidation of isopropanol to acetone. This kinetic study reveals that the oxidation of isopropanol to acetone follows the L-H mechanism.

  12. Effect of boron oxide on the cubic-to-monoclinic phase transition in yttria-stabilized zirconia

    International Nuclear Information System (INIS)

    Florio, D.Z. de; Muccillo, R.

    2004-01-01

    Specimens of yttria fully stabilized zirconia with different amounts of boron oxide have been studied by X-ray diffraction at room temperature and at higher temperatures up to 1250 deg. C. A boron oxide-assisted cubic-to-monoclinic phase transformation was determined in the temperature range 800-1250 deg. C. In situ high temperature X-ray diffraction experiments gave evidences of the dependence of the phase transformation on the heating rate. The possibility of tuning the cubic-monoclinic phase ratio by suitable addition of boron oxide before pressing and sintering is proposed

  13. Geometric phases and hidden local gauge symmetry

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo

    2005-01-01

    The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a subclass of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases

  14. Symmetry and symmetry breaking

    International Nuclear Information System (INIS)

    Balian, R.; Lambert, D.; Brack, A.; Lachieze-Rey, M.; Emery, E.; Cohen-Tannoudji, G.; Sacquin, Y.

    1999-01-01

    The symmetry concept is a powerful tool for our understanding of the world. It allows a reduction of the volume of information needed to apprehend a subject thoroughly. Moreover this concept does not belong to a particular field, it is involved in the exact sciences but also in artistic matters. Living beings are characterized by a particular asymmetry: the chiral asymmetry. Although this asymmetry is visible in whole organisms, it seems it comes from some molecules that life always produce in one chirality. The weak interaction presents also the chiral asymmetry. The mass of particles comes from the breaking of a fundamental symmetry and the void could be defined as the medium showing as many symmetries as possible. The texts put together in this book show to a great extent how symmetry goes far beyond purely geometrical considerations. Different aspects of symmetry ideas are considered in the following fields: the states of matter, mathematics, biology, the laws of Nature, quantum physics, the universe, and the art of music. (A.C.)

  15. Investigation on pseudosymmetry, twinning and disorder in crystal structure determinations: Ba(H2O)M2III[PO3(OH)]4 (M=Fe, V) as examples

    International Nuclear Information System (INIS)

    Sun Wei; Huang Yaxi; Pan Yuanming; Mi Jinxiao

    2012-01-01

    Twinning commonly occurs in monoclinic crystals with dimensionally similar a and c axes and results in pseudo-orthorhombic symmetries with overlapping diffractions. For example, twinning in the new synthetic compound Ba(H 2 O)Fe 2 [PO 3 (OH)] 4 , which varies in space group from P2 1 to P2 1 /c with approximately equal a and c axial lengths, gives rise to a pseudosymmetry of C222 1 . Similarly, the related compound Ba(H 2 O)V 2 [PO 3 (OH)] 4 is commonly twinned and varies in space groups as well, arising from ordered to disordered distributions of the barium cations and water molecules in the cavities. Moreover, analyses of these and other twinned structures show that the small average standard uncertainty of bond distances is a sensitive criterion for structure determinations, especially for those involving crystal twinning as well as order–disorder. A proper structure determination leads to small standard uncertainties of the atomic displacement parameters, which further result in the small standard uncertainties of bond distances. - Graphical abstract: Ba(H 2 O)M 2 III [PO 3 (OH)] 4 (M=Fe, V) varies in space group from P2 1 to P2 1 /c, arising from ordered to disordered distributions of Ba 2+ and H 2 O in the cavities. Highlights: ► Twinning commonly occurs in monoclinic crystals with a≈c. ► Overlapping diffractions from twin domains hamper with the determination of real space groups. ► Conventional criteria for evaluating the real space groups are not effective in this case. ► Small standard uncertainty of bond distances is proposed as a sensitive criterion. ► Using this criterion we determined the order–disorder structures of Ba(H 2 O)M 2 III [PO 3 (OH)] 4 (M=Fe, V) from twinned crystals.

  16. Creation and development of the universe (symmetry approach)

    International Nuclear Information System (INIS)

    Zheludev, I.S.

    1993-09-01

    The model according to which space subreality and time subreality are created during Big Bang is introduced. The first one is centrosymmetrical, the second anticentrosymmetrical. One to another they are transformed by mutual ''replacement'' space and time. Such subrealities are not antisubrealities and their elementary particles (appeared through Big Bang) are not able to annihilate completely because of symmetry conditions. This leads to the appearance of condensed matter. The model of two subrealities gives the possibility to explain without ''parity violation'' any physical phenomena. Four macroscopic rules of symmetry [scale, corkscrew, gyroscope and right (left) hand] reflect four fundamental interactions of our reality. (author). 10 refs, 16 figs

  17. Geometry of Majorana neutrino and new symmetries

    CERN Document Server

    Volkov, G G

    2006-01-01

    Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of ...

  18. Dynamical symmetry breakdown in SU(5) and SO(10)

    International Nuclear Information System (INIS)

    Shellard, R.C.

    1983-09-01

    Some restrictions imposed upon Grand Unified Theories by dynamical symmetry breakdown are examined. It is observed in particular, that theories with SU(5) as symmetry group, with 3 or more fermion families undergo dynamical symmetry breakdown, and some of the fermions will acquire mass at the Grand Unified scale. On the other hand, the SO(10) group, with 3 families is free from this problem. (Author) [pt

  19. Development of Xi'an-CI package – applying the hole–particle symmetry in multi-reference electronic correlation calculations

    Science.gov (United States)

    Suo, Bingbing; Lei, Yibo; Han, Huixian; Wang, Yubin

    2018-04-01

    This mini-review introduces our works on the Xi'an-CI (configuration interaction) package using graphical unitary group approach (GUGA). Taking advantage of the hole-particle symmetry in GUGA, the Galfand states used to span the CI space are classified into CI subspaces according to the number of holes and particles, and the coupling coefficients used to calculate Hamiltonian matrix elements could be factorised into the segment factors in the hole, active and external spaces. An efficient multi-reference CI with single and double excitations (MRCISD) algorithm is thus developed that reduces the storage requirement and increases the number of correlated electrons significantly. The hole-particle symmetry also gives rise to a doubly contracted MRCISD approach. Moreover, the internally contracted Gelfand states are defined within the CI subspace arising from the hole-particle symmetry, which makes the implementation of internally contracted MRCISD in the framework of GUGA possible. In addition to MRCISD, the development of multi-reference second-order perturbation theory (MRPT2) also benefits from the hole-particle symmetry. A configuration-based MRPT2 algorithm is proposed and extended to the multi-state n-electron valence-state second-order perturbation theory.

  20. Quantum groups: Geometry and applications

    International Nuclear Information System (INIS)

    Chu, C.S.

    1996-01-01

    The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge

  1. Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces

    Directory of Open Access Journals (Sweden)

    Przemysław Górka

    2014-01-01

    Full Text Available We continue our research on Sobolev spaces on locally compact abelian (LCA groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lp-spaces.

  2. Unique Piezoelectric Properties of the Monoclinic Phase in Pb (Zr ,Ti )O3 Ceramics: Large Lattice Strain and Negligible Domain Switching

    Science.gov (United States)

    Fan, Longlong; Chen, Jun; Ren, Yang; Pan, Zhao; Zhang, Linxing; Xing, Xianran

    2016-01-01

    The origin of the excellent piezoelectric properties at the morphotropic phase boundary is generally attributed to the existence of a monoclinic phase in various piezoelectric systems. However, there exist no experimental studies that reveal the role of the monoclinic phase in the piezoelectric behavior in phase-pure ceramics. In this work, a single monoclinic phase has been identified in Pb (Zr ,Ti )O3 ceramics at room temperature by in situ high-energy synchrotron x-ray diffraction, and its response to electric field has been characterized for the first time. Unique piezoelectric properties of the monoclinic phase in terms of large intrinsic lattice strain and negligible domain switching have been observed. The extensional strain constant d33 and the transverse strain constant d31 are calculated to be 520 and -200 pm /V , respectively. These large piezoelectric coefficients are mainly due to the large intrinsic lattice strain, with very little extrinsic contribution from domain switching. The unique properties of the monoclinic phase provide new insights into the mechanisms responsible for the piezoelectric properties at the morphotropic phase boundary.

  3. Unique Piezoelectric Properties of the Monoclinic Phase in Pb(Zr,Ti)O_{3} Ceramics: Large Lattice Strain and Negligible Domain Switching.

    Science.gov (United States)

    Fan, Longlong; Chen, Jun; Ren, Yang; Pan, Zhao; Zhang, Linxing; Xing, Xianran

    2016-01-15

    The origin of the excellent piezoelectric properties at the morphotropic phase boundary is generally attributed to the existence of a monoclinic phase in various piezoelectric systems. However, there exist no experimental studies that reveal the role of the monoclinic phase in the piezoelectric behavior in phase-pure ceramics. In this work, a single monoclinic phase has been identified in Pb(Zr,Ti)O_{3} ceramics at room temperature by in situ high-energy synchrotron x-ray diffraction, and its response to electric field has been characterized for the first time. Unique piezoelectric properties of the monoclinic phase in terms of large intrinsic lattice strain and negligible domain switching have been observed. The extensional strain constant d_{33} and the transverse strain constant d_{31} are calculated to be 520 and -200  pm/V, respectively. These large piezoelectric coefficients are mainly due to the large intrinsic lattice strain, with very little extrinsic contribution from domain switching. The unique properties of the monoclinic phase provide new insights into the mechanisms responsible for the piezoelectric properties at the morphotropic phase boundary.

  4. Topotactic reduction and phase transitions in (T,T′ La1.8Pr0.2CuO4

    Directory of Open Access Journals (Sweden)

    M.I. Houchati

    2017-05-01

    The X-ray powder diffraction data have revealed that this cuprate is crystallized with the so-called “pseudo-S” type structure, showing a monoclinic symmetry and space group A2/m. Concerning the EPR measurements, they have shown the presence of Cu2+ cation and a hyperfine structure suggesting a pronounced hybridization of the copper–oxygen bond. Finally, X-ray diffraction has demonstrated that the obtained La1.8Pr0.2CuO3.5, heated in oxygen at 420 °C, turns topotactically into La1.8Pr0.2CuO4 with a T′-type structure (I4/mmm.

  5. Dual realizations of dynamical symmetry breaking

    International Nuclear Information System (INIS)

    Dudas, Emilian; Papineau, Chloe

    2006-01-01

    We show the infrared equivalence between a recently proposed model containing a six dimensional scalar field with a four-dimensional localized Higgs type potential and the four-dimensional Nambu-Jona-Lasinio (NJL) model. In the dual NJL description, the fermions are localized at the origin of a large two-dimensional compact space. Due to a classical running effect above the compactification scale, the four-fermion coupling of the NJL model increases from the cutoff scale down to the compactification scale, providing the large Fermi coupling needed for the dynamical symmetry breaking. We also present a string theory embedding of our field-theory construction. On more general grounds, our results suggest that 4d models with dynamical symmetry breaking can be given a higher dimensional description in terms of field theories with nontrivial boundary conditions in the internal space

  6. Cohomology for Lagrangian systems and Noetherian symmetries

    International Nuclear Information System (INIS)

    Popp, O.T.

    1989-06-01

    Using the theory of sheaves we find some exact sequences describing the locally Lagrangian systems. Using cohomology theory of groups with coefficients in sheaves we obtain some exact sequences describing the Noetherian symmetries. It is shown how the results can be used to find all locally Lagrangian dynamics Noetherian invariant with respect to a given group of kinematical symmetries.(author)

  7. Noncommutative phase spaces on Aristotle group

    Directory of Open Access Journals (Sweden)

    Ancille Ngendakumana

    2012-03-01

    Full Text Available We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally introduced magnetic eld. These cases correspond to the minimal coupling of the momentum with a magnetic potential.

  8. Retabulation of space group extinctions for electron diffraction

    International Nuclear Information System (INIS)

    Goodman, P.; Tanaka, M.

    1989-01-01

    The space group tables previously published by one of the authors and others are here presented in a revised and compacted form designed to make for compatability with existing tables for X-ray diffraction. 136 of the 230 space groups are subject to dynamic extinctions due to glide planes and screw axes, and the observables from these space groups in specific settings are tabulated. Tabs

  9. Dark Energy and Spacetime Symmetry

    Directory of Open Access Journals (Sweden)

    Irina Dymnikova

    2017-03-01

    Full Text Available The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value.

  10. Group structure and group process for effective space station astronaut teams

    Science.gov (United States)

    Nicholas, J. M.; Kagan, R. S.

    1985-01-01

    Space Station crews will encounter new problems, many derived from the social interaction of groups working in space for extended durations. Solutions to these problems must focus on the structure of groups and the interaction of individuals. A model of intervention is proposed to address problems of interpersonal relationships and emotional stress, and improve the morale, cohesiveness, and productivity of astronaut teams.

  11. Student Facebook groups as a third space

    DEFF Research Database (Denmark)

    Aaen, Janus Holst; Dalsgaard, Christian

    2016-01-01

    -institutional, personal space of the Facebook network. The main study of the article examines six student-managed Facebook groups and provides an analysis of a total of 2247 posts and 12,217 comments. Furthermore, the study draws on group interviews with students from 17 Danish upper secondary schools and a survey......The paper examines educational potentials of Facebook groups that are created and managed by students without any involvement from teachers. The objective is to study student-managed Facebook groups as a ‘third space' between the institutional space of teacher-managed Facebook groups and the non...... answered by 932 students from 25 schools. Based on the survey and interviews, the paper concludes that Facebook is an important educational tool for students in Danish upper secondary schools to receive help on homework and assignments. Furthermore, on the basis of the analysis of Facebook groups...

  12. Noncommutative spaces and Poincaré symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, Stjepan, E-mail: meljanac@irb.hr [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia); Meljanac, Daniel [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia); Mercati, Flavio [Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Pikutić, Danijel [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia)

    2017-03-10

    We present a framework which unifies a large class of noncommutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Lorentz transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular the Lorentz group element which acts on the left and on the right of a composition of two momenta is different, and depends on the momenta involved in the process. We conclude with two representative examples, which illustrate the mentioned effect.

  13. Lie-algebra approach to symmetry breaking

    International Nuclear Information System (INIS)

    Anderson, J.T.

    1981-01-01

    A formal Lie-algebra approach to symmetry breaking is studied in an attempt to reduce the arbitrariness of Lagrangian (Hamiltonian) models which include several free parameters and/or ad hoc symmetry groups. From Lie algebra it is shown that the unbroken Lagrangian vacuum symmetry can be identified from a linear function of integers which are Cartan matrix elements. In broken symmetry if the breaking operators form an algebra then the breaking symmetry (or symmetries) can be identified from linear functions of integers characteristic of the breaking symmetries. The results are applied to the Dirac Hamiltonian of a sum of flavored fermions and colored bosons in the absence of dynamical symmetry breaking. In the partially reduced quadratic Hamiltonian the breaking-operator functions are shown to consist of terms of order g 2 , g, and g 0 in the color coupling constants and identified with strong (boson-boson), medium strong (boson-fermion), and fine-structure (fermion-fermion) interactions. The breaking operators include a boson helicity operator in addition to the familiar fermion helicity and ''spin-orbit'' terms. Within the broken vacuum defined by the conventional formalism, the field divergence yields a gauge which is a linear function of Cartan matrix integers and which specifies the vacuum symmetry. We find that the vacuum symmetry is chiral SU(3) x SU(3) and the axial-vector-current divergence gives a PCAC -like function of the Cartan matrix integers which reduces to PCAC for SU(2) x SU(2) breaking. For the mass spectra of the nonets J/sup P/ = 0 - ,1/2 + ,1 - the integer runs through the sequence 3,0,-1,-2, which indicates that the breaking subgroups are the simple Lie groups. Exact axial-vector-current conservation indicates a breaking sum rule which generates octet enhancement. Finally, the second-order breaking terms are obtained from the second-order spin tensor sum of the completely reduced quartic Hamiltonian

  14. Symmetry of priapulids (Priapulida). 1. Symmetry of adults.

    Science.gov (United States)

    Adrianov, A V; Malakhov, V V

    2001-02-01

    Priapulids possess a radial symmetry that is remarkably reflected in both external morphology and internal anatomy. It results in the appearance of 25-radial (a number divisible by five) symmetry summarized as a combination of nonaradial, octaradial, and octaradial (9+8+8) symmetries of scalids. The radial symmetry is a secondary appearance considered as an evolutionary adaptation to a lifestyle within the three-dimensional environment of bottom sediment. The eight anteriormost, or primary, scalids retain their particular position because of their innervation directly from the circumpharyngeal brain. As a result of a combination of the octaradial symmetry of primary scalids, pentaradial symmetry of teeth, and the 25-radial symmetry of scalids, the initial bilateral symmetry remains characterized by the single sagittal plane. Copyright 2001 Wiley-Liss, Inc.

  15. Statistical symmetries in physics

    International Nuclear Information System (INIS)

    Green, H.S.; Adelaide Univ., SA

    1994-01-01

    Every law of physics is invariant under some group of transformations and is therefore the expression of some type of symmetry. Symmetries are classified as geometrical, dynamical or statistical. At the most fundamental level, statistical symmetries are expressed in the field theories of the elementary particles. This paper traces some of the developments from the discovery of Bose statistics, one of the two fundamental symmetries of physics. A series of generalizations of Bose statistics is described. A supersymmetric generalization accommodates fermions as well as bosons, and further generalizations, including parastatistics, modular statistics and graded statistics, accommodate particles with properties such as 'colour'. A factorization of elements of ggl(n b ,n f ) can be used to define truncated boson operators. A general construction is given for q-deformed boson operators, and explicit constructions of the same type are given for various 'deformed' algebras. A summary is given of some of the applications and potential applications. 39 refs., 2 figs

  16. The symmetries and conservation laws of some Gordon-type

    Indian Academy of Sciences (India)

    Conservation laws; Milne space-time; Gordon-type equations. Abstract. In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented ... Pramana – Journal of Physics | News.

  17. SYMMETRY CLASSIFICATION OF NEWTONIAN INCOMPRESSIBLEFLUID’S EQUATIONS FLOW IN TURBULENT BOUNDARY LAYERS

    Directory of Open Access Journals (Sweden)

    Nadjafikhah M.

    2017-07-01

    Full Text Available Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.

  18. Rigidity and symmetry

    CERN Document Server

    Weiss, Asia; Whiteley, Walter

    2014-01-01

    This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme.  Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology.  The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and gradu...

  19. Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.

    Science.gov (United States)

    Adrianov, A V; Malakhov, V V

    2001-02-01

    Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment. Copyright 2001 Wiley-Liss, Inc.

  20. Chiral symmetry breaking and confinement in Minkowski space QED2+1

    International Nuclear Information System (INIS)

    Sauli, V.; Batiz, Z.

    2010-01-01

    Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e. g. with the standard Euclidean calculation. We have presented for the first analysis of the electron gap equation in Minkowski and Temporal Euclidean space. The dynamical generation of imaginary part of the fermion mass leads to the absence of Khallen-Lehmann representation, providing thus confining solution for all value of m. Apart very small κ the real pole in the propagator is absent as well. Similarly to Euclidean QED3 Minkowski QED2+1 exhibits spontaneous chiral symmetry breaking the mass function has nontrivial solution in the limit m = 0, however the mass is complex function. Furthermore, we compare with QED solved in similar approximation in spacelike Euclidean and Temporal Euclidean space. As a interesting results, although based on the simple ladder approximation, is the proof of the exact equivalence between the theories defined in Minkowski 2+1 and 3D Temporal Euclidean space. We expect large quantitative changes when the polarization effect is taken account, especially the existence of critical number of flavors can be different when compared to the known Euclidean space estimates. Opposite to naive belief we showed and explained that the Wick rotation -the well known calculational trick in quantum theory- provides continuation of Schwinger function of the Euclidean theory which do not correspond with the Greens function calculated directly in the original Minkowski space. We can note our finding has a little to do with the know usefulness of various

  1. Coset models and D-branes in group manifolds

    International Nuclear Information System (INIS)

    Orlando, Domenico

    2006-01-01

    We conjecture the existence of a duality between heterotic closed strings on homogeneous spaces and symmetry-preserving D-branes on group manifolds, based on the observation about the coincidence of the low-energy field description for the two theories. For the closed string side we also give an explicit proof of a no-renormalization theorem as a consequence of a hidden symmetry and infer that the same property should hold true for the higher order terms of the dbi action

  2. Lattice chiral symmetry and the Wess-Zumino model

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo; Ishibashi, Masato

    2002-01-01

    A lattice regularization of the supersymmetric Wess-Zumino model is studied by using Ginsparg-Wilson operators. We recognize a certain conflict between the lattice chiral symmetry and the Majorana condition for Yukawa couplings, or in Weyl representation a conflict between the lattice chiral symmetry and Yukawa couplings. This conflict is also related, though not directly, to the fact that the kinetic (Kaehler) term and the superpotential term are clearly distinguished in the continuum Wess-Zumino model, whereas these two terms are mixed in the Ginsparg-Wilson operators. We illustrate a case where lattice chiral symmetry together with naive Bose-Fermi symmetry is imposed by preserving a SUSY-like symmetry in the free part of the Lagrangian; one-loop level non-renormalization of the superpotential is then maintained for finite lattice spacing, though the finite parts of wave function renormalization deviate from the supersymmetric value. All these properties hold for the general Ginsparg-Wilson algebra independently of the detailed construction of lattice Dirac operators

  3. Mixed symmetry tensors in the worldline formalism

    Energy Technology Data Exchange (ETDEWEB)

    Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)

    2016-05-10

    We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

  4. Spontaneous compactification of space in an Einstein-Yang-Mills-Higgs model

    International Nuclear Information System (INIS)

    Cremmer, E.; Scherk, J.

    1976-01-01

    It is shown that classical solutions of an Einstein-Yang-Mills-Higgs system exist such that space-time is the direct product of the Minkowski space by a compact internal space of constant curvature. The symmetry group of the internal space determines the masses in such a way that singlets have the lowest energy, non-singlet states having huge masses. (Auth.)

  5. Flavour from accidental symmetries

    International Nuclear Information System (INIS)

    Ferretti, Luca; King, Stephen F.; Romanino, Andrea

    2006-01-01

    We consider a new approach to fermion masses and mixings in which no special 'horizontal' dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries

  6. Quantized Response and Topological Magnetic Insulators with Inversion Symmetry

    NARCIS (Netherlands)

    Turner, A.M.; Zhang, Y.; Mong, R.S.K.; Vishwanath, A.

    2012-01-01

    We study three-dimensional insulators with inversion symmetry in which other point group symmetries, such as time reversal, are generically absent. We find that certain information about such materials’ behavior is determined by just the eigenvalues under inversion symmetry of occupied states at

  7. Patterns of symmetry breaking in chiral QCD

    Science.gov (United States)

    Bolognesi, Stefano; Konishi, Kenichi; Shifman, Mikhail

    2018-05-01

    We consider S U (N ) Yang-Mills theory with massless chiral fermions in a complex representation of the gauge group. The main emphasis is on the so-called hybrid ψ χ η model. The possible patterns of realization of the continuous chiral flavor symmetry are discussed. We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group (complete or partial) by bifermion condensates. As a result a color-flavor locked symmetry is preserved. The 't Hooft anomaly matching proceeds via saturation of triangles by massless composite fermions or, in a mixed mode, i.e. also by the "weakly" coupled fermions associated with dynamical Abelianization, supplemented by a number of Nambu-Goldstone mesons. Gauge-singlet condensates are of the multifermion type and, though it cannot be excluded, the chiral symmetry realization via such gauge invariant condensates is more contrived (requires a number of four-fermion condensates simultaneously and, even so, problems remain) and less plausible. We conclude that in the model at hand, chiral flavor symmetry implies dynamical Higgsing by bifermion condensates.

  8. Gauging the graded conformal group with unitary internal symmetries

    International Nuclear Information System (INIS)

    Ferrara, S.; Townsend, P.K.; Kaku, M.; Nieuwenhuizen Van, P.

    1977-06-01

    Gauge theories for extended SU(N) conformal supergravity are constructed which are invariant under local scale, chiral, proper conformal, supersymmetry and internal SU(N) transformations. The relation between intrinsic parity and symmetry properties of their generators of the internal vector mesons is established. These theories contain no cosmological constants, but technical problems inherent to higher derivative actions are pointed out

  9. Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na4Ir3O8

    Science.gov (United States)

    Huang, Biao; Kim, Yong Baek; Lu, Yuan-Ming

    2017-02-01

    Na4Ir3O8 provides a material platform to study three-dimensional quantum spin liquids in the geometrically frustrated hyperkagome lattice of Ir4 + ions. In this work, we consider quantum spin liquids on a hyperkagome lattice for generic spin models, focusing on the effects of anisotropic spin interactions. In particular, we classify possible Z2 and U (1 ) spin liquid states, following the projective symmetry group analysis in the slave-fermion representation. There are only three distinct Z2 spin liquids, together with 2 different U (1 ) spin liquids. The nonsymmorphic space group symmetry of the hyperkagome lattice plays a vital role in simplifying the classification, forbidding "π -flux" or "staggered-flux" phases in contrast to symmorphic space groups. We further prove that both U (1 ) states and one Z2 state among all 3 are symmetry-protected gapless spin liquids, robust against any symmetry-preserving perturbations. Motivated by the "spin-freezing" behavior recently observed in Na4Ir3O8 at low temperatures, we further investigate the nearest-neighbor spin model with the dominant Heisenberg interaction subject to all possible anisotropic perturbations from spin-orbit couplings. We find that a U (1 ) spin liquid ground state with spinon Fermi surfaces is energetically favored over Z2 states. Among all spin-orbit coupling terms, we show that only the Dzyaloshinskii-Moriya interaction can induce spin anisotropy in the ground state when perturbing from the isotropic Heisenberg limit. Our work paves the way for a systematic study of quantum spin liquids in various materials with a hyperkagome crystal structure.

  10. Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton

    International Nuclear Information System (INIS)

    Julia, B.; Nicolai, H.

    1996-08-01

    General relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra A 1 (1) and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semi-direct product of Lie(A 1 (1) ) by the Witt algebra Lie(W). Furthermore we exhibit the corresponding hidden gauge symmetries. We show that the theory can be understood in terms of an infinite dimensional potential space involving all degrees of freedom: The dilaton as well as matter and gravitation. In the dilaton sector the linear system that extends the previously known Lax pair has the form of a twisted self-duality constraint that is the analog of the self-duality constraint arising in extended supergravities in higher spacetime dimensions. Our results furnish a group theoretical explanation for the simultaneous occurrence of two spectral parameters, a constant one (=y) and a variable one (=t). They hold for all 2d non-linear σ-models that are obtained by dimensional reduction of G/H models in three dimensions coupled to pure gravity. In that case the Lie algebra is Lie(W∝G (1) ); this symmetry acts on a set of off shell fields (in a fixed gauge) and preserves the equations of motion. (orig.)

  11. Anomalies of hidden local chiral symmetries in sigma-models and extended supergravities

    International Nuclear Information System (INIS)

    Vecchia, P. di; Ferrara, S.; Girardello, L.

    1985-01-01

    Non-linear sigma-models with hidden gauge symmetries are anomalous, at the quantum level, when coupled to chiral fermions in not anomaly free representations of the hidden chiral symmetry. These considerations generally apply to supersymmetric kaehlerian sigma-models on coset spaces with hidden chiral symmetries as well as to extended supergravities in four dimensions with local SU(N) symmetry. The presence of the anomaly implies that the scenario of dynamical generation of gauge vector bosons has to be reconsidered in these theories. (orig.)

  12. Conformal maps and group contractions in nuclear structure

    International Nuclear Information System (INIS)

    Bonatsos, D.

    2011-01-01

    In mathematics, a conformal map is a function which preserves angles. We show how this procedure can be used in the framework of the Bohr Hamiltonian, leading to a Hamiltonian in a curved space, in which the mass depends on the nuclear deformation β, while it remains independent of the collective variable γ and the three Euler angles. This Hamiltonian is proved to be equivalent to that obtained using techniques of Supersymmetric Quantum Mechanics. Group contraction is a procedure in which a symmetry group is reduced into a group of lower symmetry in a certain limiting case. Examples are provided in the large boson number limit of the Interacting Boson Approximation (IBA) model by a) the contraction of the SU(3) algebra into the [R 5 ]SO(3) algebra of the rigid rotator, consisting of the angular momentum operators forming SO(3), plus 5 mutually commuting quantities, the quadrupole operators, b) the contraction of the O(6) algebra into the [R 5 ]SO(5) algebra of the γ-unstable rotator. We show how contractions can be used for constructing symmetry lines in the interior of the symmetry triangle of the IBA model. (author)

  13. Electroweak symmetry breaking in supersymmetric gauge-Higgs unification models

    International Nuclear Information System (INIS)

    Choi, Kiwoon; Jeong, Kwang-Sik; Okumura, Ken-ichi; Haba, Naoyuki; Shimizu, Yasuhiro; Yamaguchi, Masahiro

    2004-01-01

    We examine the Higgs mass parameters and electroweak symmetry breaking in supersymmetric orbifold field theories in which the 4-dimensional Higgs fields originate from higher-dimensional gauge supermultiplets. It is noted that such gauge-Higgs unification leads to a specific boundary condition on the Higgs mass parameters at the compactification scale, which is independent of the details of supersymmetry breaking mechanism. With this boundary condition, phenomenologically viable parameter space of the model is severely constrained by the condition of electroweak symmetry breaking for supersymmetry breaking scenarios which can be realized naturally in orbifold field theories. For instance, if it is assumed that the 4-dimensional effective theory is the minimal supersymmetric standard model with supersymmetry breaking parameters induced by the Scherk-Schwarz mechanism, a correct electroweak symmetry breaking can not be achieved for reasonable range of parameters of the model, even when one includes additional contributions to the Higgs mass parameters from the auxiliary component of 4-dimensional conformal compensator. However if there exists a supersymmetry breaking mediated by brane superfields, sizable portion of the parameter space can give a correct electroweak symmetry breaking. (author)

  14. Symmetry chains and adaptation coefficients

    International Nuclear Information System (INIS)

    Fritzer, H.P.; Gruber, B.

    1985-01-01

    Given a symmetry chain of physical significance it becomes necessary to obtain states which transform properly with respect to the symmetries of the chain. In this article we describe a method which permits us to calculate symmetry-adapted quantum states with relative ease. The coefficients for the symmetry-adapted linear combinations are obtained, in numerical form, in terms of the original states of the system and can thus be represented in the form of numerical tables. In addition, one also obtains automatically the matrix elements for the operators of the symmetry groups which are involved, and thus for any physical operator which can be expressed either as an element of the algebra or of the enveloping algebra. The method is well suited for computers once the physically relevant symmetry chain, or chains, have been defined. While the method to be described is generally applicable to any physical system for which semisimple Lie algebras play a role we choose here a familiar example in order to illustrate the method and to illuminate its simplicity. We choose the nuclear shell model for the case of two nucleons with orbital angular momentum l = 1. While the states of the entire shell transform like the smallest spin representation of SO(25) we restrict our attention to its subgroup SU(6) x SU(2)/sub T/. We determine the symmetry chains which lead to total angular momentum SU(2)/sub J/ and obtain the symmetry-adapted states for these chains

  15. Kac-Moody algebra is not hidden symmetry of chiral models

    International Nuclear Information System (INIS)

    Devchand, C.; Schiff, J.

    1997-01-01

    A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional Abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. (author). 15 refs

  16. Deriving GENERIC from a Generalized Fluctuation Symmetry

    Science.gov (United States)

    Kraaij, Richard; Lazarescu, Alexandre; Maes, Christian; Peletier, Mark

    2018-02-01

    Much of the structure of macroscopic evolution equations for relaxation to equilibrium can be derived from symmetries in the dynamical fluctuations around the most typical trajectory. For example, detailed balance as expressed in terms of the Lagrangian for the path-space action leads to gradient zero-cost flow. We expose a new such fluctuation symmetry that implies GENERIC, an extension of gradient flow where a Hamiltonian part is added to the dissipative term in such a way as to retain the free energy as Lyapunov function.

  17. Symmetry breaking in the opinion dynamics of a multi-group project organization

    International Nuclear Information System (INIS)

    Zhu Zhen-Tao; Zhou Jing; Chen Xing-Guang; Li Ping

    2012-01-01

    A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces: (i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness. Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes, i.e., a deadlock regime, a convergence regime, and a bifurcation regime in opinion dynamics. The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to. In the case of a three-group project with a symmetric social network, both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord, instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p. 125 Fig. 5), project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations, which urges that apart from divergence in participants' interests, nonlinear interaction can also make conflict inevitable in the PO. The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO. It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO

  18. Symmetry breaking in the opinion dynamics of a multi-group project organization

    Science.gov (United States)

    Zhu, Zhen-Tao; Zhou, Jing; Li, Ping; Chen, Xing-Guang

    2012-10-01

    A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces: (i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness. Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes, i.e., a deadlock regime, a convergence regime, and a bifurcation regime in opinion dynamics. The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to. In the case of a three-group project with a symmetric social network, both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord, instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p. 125 Fig. 5), project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations, which urges that apart from divergence in participants' interests, nonlinear interaction can also make conflict inevitable in the PO. The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO. It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.

  19. Lie symmetries and superintegrability

    International Nuclear Information System (INIS)

    Nucci, M C; Post, S

    2012-01-01

    We show that a known superintegrable system in two-dimensional real Euclidean space (Post and Winternitz 2011 J. Phys. A: Math. Theor. 44 162001) can be transformed into a linear third-order equation: consequently we construct many autonomous integrals—polynomials up to order 18—for the same system. The reduction method and the connection between Lie symmetries and Jacobi last multiplier are used.

  20. Symmetry breaking in a five-dimensional SU(5) model

    International Nuclear Information System (INIS)

    Svetovoi, V.B.; Khariton, N.G.

    1986-01-01

    Two-state symmetry breaking in a SU(5) model in a space with M 4 x S 1 topology is discussed. The scalar 24-plet is a component of a five-vector and acquires a nonzero vacuum expectation value at the quantum level. The vacuum differs substantially from that of the standard SU(5) model. Its orientation in the SU(5) space and absolute magnitude are fixed uniquely. The second stage of the symmetry breaking occurs on account of a five-scalar in the fundamental representation of SU(5) by means of the Weinberg mechanism. The small mass of the scalar SU(2) doublet is not explained

  1. On the origin of neutrino flavour symmetry

    International Nuclear Information System (INIS)

    King, Stephen F.; Luhn, Christoph

    2009-01-01

    We study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such 'indirect' models we discuss the D-term flavon vacuum alignments which are required for such an accidental flavour symmetry consistent with tri-bimaximal lepton mixing to emerge. We identify large classes of suitable discrete family symmetries, namely the Δ(3n 2 ) and Δ(6n 2 ) groups, together with other examples such as Z 7 x Z 3 . In such indirect models the implementation of the type I see-saw mechanism is straightforward using constrained sequential dominance. However the accidental neutrino flavour symmetry may be easily violated, for example leading to a large reactor angle, while maintaining accurately the tri-bimaximal solar and atmospheric predictions.

  2. Infrared studies of the monoclinic-tetragonal phase transition in Pb(Zr,Ti)O3 ceramics

    International Nuclear Information System (INIS)

    Guarany, C A; Pelaio, L H Z; Araujo, E B; Yukimitu, K; Moraes, J C S; Eiras, J A

    2003-01-01

    Recently, the observation of a new monoclinic phase in the PbZr 1-x Ti x O 3 (PZT) system in the vicinity of the morphotropic phase boundary was reported. Investigations of this new phase were reported using different techniques such as high-resolution synchrotron x-ray powder diffraction and Raman spectroscopy. In this work, the monoclinic → tetragonal phase transition in PbZr 0.50 Ti 0.50 O 3 ceramics was studied using infrared spectroscopy between 1000 and 400 cm -1 . The four possible ν 1 -stretching modes (Ti-O and Zr-O stretch) in the BO 6 octahedron in the ABO 3 structure of PZT in this region were monitored as a function of temperature. The lower-frequency mode ν 1 -(Zr-O) remains practically unaltered, while both intermediate ν 1 -(Ti-O) modes decrease linearly as temperature increases from 89 to 263 K. In contrast, the higher-frequency ν 1 -(Ti-O) and ν 1 -(Zr-O) modes present anomalous behaviour around 178 K. The singularity observed at this mode was associated with the monoclinic → tetragonal phase transition in PbZr 0.50 Ti 0.50 O 3 ceramics

  3. Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the Gyroid wire network

    Energy Technology Data Exchange (ETDEWEB)

    Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit

    2012-08-15

    Motivated by Harper Hamiltonians on skeletal graphs and their C{sup *}-geometry, we study a certain class of graph Hamiltonians. These Hamiltonians can be thought of as a finite groupoid representation in separable Hilbert spaces. Here the groupoid is the path groupoid of a finite graph. Given such a setup, we consider the possible matrix versions of the Hamiltonian, which are indexed by the choice of a rooted spanning tree and an order of the vertices. The first result is that all the matrix representations are linked to each other via the conjugation action of a re-gauging groupoid. We furthermore show that the symmetries of the underlying graph give rise to an action on the Hamiltonians of a group of extended symmetries. The new concept for the extension is to allow phase transformations on the vertices. In the commutative case, we prove that the extended symmetries act via a projective representation giving rise to isotypical decompositions and super-selection rules. We then apply these results to the PDG and honeycomb graphs using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the Gyroid and the honeycomb.

  4. Contact symmetries and Hamiltonian thermodynamics

    International Nuclear Information System (INIS)

    Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

    2015-01-01

    It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production

  5. Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics

    International Nuclear Information System (INIS)

    El Naschie, M.S.

    2008-01-01

    We are constructing a hierarchy of kissing numbers representing singular contact points of hyper-spheres in exceptional Lie symmetry groups lattice arrangement embedded in the 26 dimensional bosonic strings spacetime. That way we find a total number of points and dimensions equal to 548. This is 52 more than the order of E 8 E 8 of heterotic string theory and leads to the prediction of 69 elementary particles at an energy scale under 1 T. In other words, our mathematical model predicts nine more particles than what is currently experimentally known to exist in the standard model of high energy physics namely only 60. The result is thus in full agreement with all our previous theoretical findings

  6. The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry

    Science.gov (United States)

    He, Wen-Yu; Chan, C. T.

    2015-01-01

    We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states. PMID:25640993

  7. G-Boson renormalizations and mixed symmetry states

    International Nuclear Information System (INIS)

    Scholten, O.

    1986-01-01

    In the IBA model the low-lying collective states are described in terms of a system of interacting s- and d-bosons. A boson can be interpreted as corresponding to collective J=0 or J=2 fermion pair states. As such the IBA model space can be seen as only a small subsector of the full shell model space. For medium heavy nuclei such a truncation of the model space is necessary to make calculations feasible. As is well known truncations of a model space make it necessary to renormalize the model parameters. In this work some renormalizations of the Hamiltonian and the E2 transition operator will be discussed. Special attention will be given to the implication of these renormalizations for the properties of mixed symmetry states. The effects of renormalization are obtained by considering the influence of fermion pair states that have been omitted from the model basis. Here the authors focus attention on the effect of the low-lying two particle J=4 state, referred to as g-boson or G-pair state. Renormalizations of the d-boson energy, the E2 effective charges, and symmetry force are discussed

  8. Hazy spaces, tangent spaces, manifolds and groups

    International Nuclear Information System (INIS)

    Dodson, C.T.J.

    1977-03-01

    The results on hazy spaces and the developments leading to hazy manifolds and groups are summarized. Proofs have appeared elsewhere so here examples are considered and some motivation for definitions and constructions in the theorems is analyzed. It is shown that quite simple ideas, intuitively acceptable, lead to remarkable similarity with the theory of differentiable manifolds. Hazy n manifolds have tangent bundles that are hazy 2n manifolds and there are hazy manifold structures for groups. Products and submanifolds are easily constructed and in particular the hazy n-sphere manifolds as submanifolds of the standard hazy manifold Zsup(n+1)

  9. On the structure and applications of the Bondi-Metzner-Sachs group

    Science.gov (United States)

    Alessio, Francesco; Esposito, Giampiero

    This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs (BMS) group. Minkowski space-time has an interesting and useful group of isometries, but, for a generic space-time, the isometry group is simply the identity and hence provides no significant informations. Yet symmetry groups have important role to play in physics; in particular, the Poincaré group describing the isometries of Minkowski space-time plays a role in the standard definitions of energy-momentum and angular-momentum. For this reason alone it would seem to be important to look for a generalization of the concept of isometry group that can apply in a useful way to suitable curved space-times. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work, the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of “asymptotic simplicity” are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the BMS group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the BMS group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the BMS invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.

  10. Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

    Directory of Open Access Journals (Sweden)

    Katy L. Chubb

    2018-04-01

    Full Text Available A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE.

  11. R-symmetries from the orbifolded heterotic string

    International Nuclear Information System (INIS)

    Schmitz, Matthias

    2014-08-01

    We examine the geometric origin of discrete R-symmetries in heterotic orbifold compactifications. By analysing the symmetries of the worldsheet instanton solutions and the underlying geometry, we obtain a scheme that allows us to systematically explore the R-symmetries arising in these compactifications. Applying this scheme to a classification of orbifold geometries, we are able to find all R-symmetries of heterotic orbifolds with Abelian point groups. We show that in the vast majority of cases, the R-symmetries found satisfy anomaly universality constraints, as required in heterotic orbifolds. Then we examine the implications of the presence of these R-symmetries on a class of phenomenologically attractive orbifold compactifications known as the heterotic mini-landscape. We use the technique of Hilbert bases in order to analyse the properties of a vacuum configuration. We find that phenomenologically viable models remain and the main attractive features of the mini-landscape are unaltered.

  12. String cohomology groups of complex projective spaces

    DEFF Research Database (Denmark)

    Ottosen, Iver; Bökstedt, Marcel

    2007-01-01

    Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. The equivariant cohomology H*(LXhT;Z/p) is a module over H*(BT;Z/p). We give a computation of this module when X=CPr for any positive integer r and any prime number p. The compu......Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. The equivariant cohomology H*(LXhT;Z/p) is a module over H*(BT;Z/p). We give a computation of this module when X=CPr for any positive integer r and any prime number p...

  13. Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata

    Directory of Open Access Journals (Sweden)

    Ikuko Tanaka

    2015-09-01

    Full Text Available To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA models under regular and random initial conditions corresponds to three Wolfram’s classes of CAs, identified as Classes II, III, and IV. Regular initial conditions occur in two groups. One group that makes a broken, regular pattern formation has four types of symmetry, whereas the other group that makes a higher hierarchy pattern formation has only two types. Additionally, both final pattern formations show an increased amount of symmetropy as time passes. Moreover, the final pattern formations are affected by iterations of base rules of CA models of chaos dynamical systems. The growth design formations limit possibilities: the ratio of developing final pattern formations under a regular initial condition decreases in the order of Classes III, II, and IV. This might be related to the difference in degree in reference to surrounding conditions. These findings suggest that calculations of symmetries of the structures of one-dimensional cellular automata models are useful for revealing rules of pattern generation for animal bodies.

  14. Crystalline and magnetic ordering in the monoclinic phase of the layered perovskite PAMC

    DEFF Research Database (Denmark)

    Harris, P.; Lebech, B.; Achiwa, N.

    1994-01-01

    A single-crystal elastic neutron scattering experiment between 4.2 and 115 K has been performed on the low-temperature monoclinic zeta phase of the layered perovskite bis(propylammonium) manganesetetrachloride (PAMC). The crystalline structure is commensurately modulated, with a modulation vector...

  15. Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum

    International Nuclear Information System (INIS)

    Duguet, T

    2015-01-01

    We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei. (paper)

  16. Diffeomorphism-type symmetries of the self-dual Yang-Mills equations

    International Nuclear Information System (INIS)

    Ivanova, T.A.

    1998-01-01

    The infinite-dimensional algebra of diffeomorphism-type symmetries of the self-dual Yang-Mills equations is described as the algebra of 0-cochains with values in a sheaf of germs of holomorphic sections of the (1,0) tangent bundle over the twistor space. It is shown that the extended conformal symmetries are obtained as particular cases of the aforementioned algebra

  17. N,N,N-Tris(diphenylphosphorylmethylamine

    Directory of Open Access Journals (Sweden)

    Olaf Walter

    2017-10-01

    Full Text Available The structure of N,N,N-tris(diphenylphosphorylmethylamine, C39H36NO3P3, at 103 K has monoclinic (P21/c symmetry. Two molecules, each with pseudo-threefold rotation symmetry, crystallize in the asymmetric unit of the monoclinic unit cell. The compound acts as ligand for the stabilization of metal ions with flexible coordination enabling three- or fourfold coordination.

  18. Symmetries of Maldacena-Wilson loops from integrable string theory

    International Nuclear Information System (INIS)

    Muenkler, Hagen

    2017-01-01

    This thesis discusses hidden symmetries within N=4 supersymmetric Yang-Mills theory or its AdS/CFT dual, string theory in AdS 5 x S 5 . Here, we focus on the Maldacena-Wilson loop, which is a suitable object for this study since its vacuum expectation value is finite for smooth contours and the conjectured duality to scattering amplitudes provides a conceptual path to transfer its symmetries to other observables. Its strong-coupling description via minimal surfaces in AdS 5 allows to construct the symmetries from the integrability of the underlying classical string theory. This approach has been utilized before to derive a strong-coupling Yangian symmetry of the Maldacena-Wilson loop and describe equiareal deformations of minimal surfaces in AdS 3 . These two findings are connected and extended in the present thesis. In order to discuss the symmetries systematically, we first discuss the symmetry structure of the underlying string model. The discussion can be generalized to the discussion of generic symmetric space models. For these, we find that the symmetry which generates the equiareal deformations of minimal surfaces in AdS 3 has a central role in the symmetry structure of the model: It acts as a raising operator on the infinite tower of conserved charges, thus generating the spectral parameter, and can be employed to construct all symmetry variations from the global symmetry of the model. It is thus referred to as the master symmetry of symmetric space models. Additionally, the algebra of the symmetry variations and the conserved charges is worked out. For the concrete case of minimal surfaces in AdS 5 , we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering amplitude. This marks the first step toward transferring the master symmetry to scattering amplitudes. Moreover, we compute the master and Yangian symmetry variations of generic, smooth boundary curves. The results leads to a coupling

  19. Symmetries of Maldacena-Wilson loops from integrable string theory

    Energy Technology Data Exchange (ETDEWEB)

    Muenkler, Hagen

    2017-09-11

    This thesis discusses hidden symmetries within N=4 supersymmetric Yang-Mills theory or its AdS/CFT dual, string theory in AdS{sub 5} x S{sup 5}. Here, we focus on the Maldacena-Wilson loop, which is a suitable object for this study since its vacuum expectation value is finite for smooth contours and the conjectured duality to scattering amplitudes provides a conceptual path to transfer its symmetries to other observables. Its strong-coupling description via minimal surfaces in AdS{sub 5} allows to construct the symmetries from the integrability of the underlying classical string theory. This approach has been utilized before to derive a strong-coupling Yangian symmetry of the Maldacena-Wilson loop and describe equiareal deformations of minimal surfaces in AdS{sub 3}. These two findings are connected and extended in the present thesis. In order to discuss the symmetries systematically, we first discuss the symmetry structure of the underlying string model. The discussion can be generalized to the discussion of generic symmetric space models. For these, we find that the symmetry which generates the equiareal deformations of minimal surfaces in AdS{sub 3} has a central role in the symmetry structure of the model: It acts as a raising operator on the infinite tower of conserved charges, thus generating the spectral parameter, and can be employed to construct all symmetry variations from the global symmetry of the model. It is thus referred to as the master symmetry of symmetric space models. Additionally, the algebra of the symmetry variations and the conserved charges is worked out. For the concrete case of minimal surfaces in AdS{sub 5}, we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering amplitude. This marks the first step toward transferring the master symmetry to scattering amplitudes. Moreover, we compute the master and Yangian symmetry variations of generic, smooth boundary curves. The results

  20. Coupling-constant flows and dynamical symmetry breaking

    International Nuclear Information System (INIS)

    Yamagishi, H.

    1981-01-01

    The Coleman-Weinberg theory is reformulated in terms of flows in coupling-constant space. It is shown that the existence of dynamical symmetry breaking is governed essentially by the b functions. An application is made to the massless Weinberg-Salam model