Jia, L Y
2016-01-01
The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work we show that this symmetry is preserved in the subspace truncated at a certain generalized seniority, and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, we study the particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and others.
Energy Level Statistics of SO(5) Limit of Super-symmetry U(6/4) in Interacting Boson-Fermion Model
无
2005-01-01
We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd-A nucleus using the interacting boson-fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (△3)are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SOB(5) and SOBF(5)and the spin play important roles in the energy level statistics, however, along with the increase of N, the statistics distribution would tend to be in Poisson form.
Tsekov, R
2016-01-01
Thermodynamically, bosons and fermions differ by their statistics only. A general entropy functional is proposed by superposition of entropic terms, typical for different quantum gases. The statistical properties of the corresponding Janus particles are derived by variation of the weight of the boson/fermion fraction. It is shown that di-bosons and anti-fermions separate in gas and liquid phases, while three-phase equilibrium appears for poly-boson/fermion Janus particles.
Inertial parameters in the interacting boson fermion approximation
The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors)
SU(8) family unification with boson-fermion balance
CERN. Geneva
2014-01-01
Grand unification has been intensively investigated for over forty years, and many different approaches have been tried. In this talk I propose a model that involves three ingredients that do not appear in the usual constructions: (1) boson--fermion balance without full supersymmetry, (2) canceling the spin 1/2 fermion gauge anomalies against the anomaly from a gauged spin 3/2 gravitino, and (3) using a scalar field representation with non-zero U(1) generator to break the SU(8) gauge symmetry through a ground state which, before dynamical symmetry breaking, has a periodic U(1) generator structure. The model has a number of promising features: (1) natural incorporation of three families, (2) incorporation of the experimentally viable flipped SU(5) model, (3) a symmetry breaking pathway to the standard model using the scalar field required by boson-fermion balance, together with a stage of most attractive channel dynamical symmetry breaking, without postulating additional Higgs fields, (4) vanishing of bare Yuk...
Plethystic Vertex Operators and Boson-Fermion Correspondences
Fauser, Bertfried; King, Ronald C
2016-01-01
We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape \\pi. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each \\pi, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.
Massive Boson-Fermion Degeneracy and the Early Structure of the Universe
Kounnas, Costas
2008-01-01
The existence of a new kind of massive boson-fermion symmetry is shown explicitly in the framework of the heterotic, type II and type II orientifold superstring theories. The target space-time is two-dimensional. Higher dimensional models are defined via large marginal deformations of JxJ-type. The spectrum of the initial undeformed two dimensional vacuum consists of massless boson degrees of freedom, while all massive boson and fermion degrees of freedom exhibit a new Massive Spectrum Degene...
SU(8) unification with boson-fermion balance
Adler, Stephen L
2014-01-01
We formulate an $SU(8)$ unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson--fermion balance. Gauge field $SU(8)$ anomalies cancel between the gravitinos and spin $\\frac {1}{2}$ fermions. The 56 of scalars breaks $SU(8)$ to $SU(3)_{family} \\times SU(5)/Z_5$, with the fermion representation content needed for ``flipped'' $SU(5)$, and with the residual scalars in the representations needed for further gauge symmetry breaking to the standard model. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries. In the limit of vanishing gauge coupling, there are $N=1$ and $N=8$ supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and ``calculable''. In an Appendix we give an analysis of symmetry breaking by a Higgs component,...
Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation
A new boson-fermion model of superconductivity
De Cao, Tian
2010-01-01
It is shown that the superconducting energy gap necessarily lead to the disappearance of some quasi-electrons, thus we suggest a new boson-fermion Hamiltonian to describe superconductivity. The new supercurrent equations are derived with this Hamiltonian. Some new results can be found besides the zero resistance effect, the Meissner effect and the magnetic flux quantum can be explained.
Reciprocal Symmetric Boltzmann Function and Unified Boson-Fermion Statistics
Ahmad, Mushfiq; Talukder, Muhammad O. G.
2007-01-01
The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The solutions of this equation come in Boson-Fermion pairs. Reciprocal symmetric Boltzmann's function, thus, unifies both Bosonic and Fermionic distributions.
Functional Integrals and Collective Excitations in Boson-Fermion Model
YAN Jun
2006-01-01
In this paper, collective excitations in the boson-fermion model are investigated by means of functional integration method. The equations of energy gap and excitation spectrum are derived. Moreover, the Bose energy spectrum of zero wave vector Fermi fields is also calculated.
Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two such correspondences are well known: the types A and B (and their super extensions). As a main result of this paper we present a new boson-fermion correspondence of type D-A. Further, we define a new concept of twisted vertex algebra of order N, which generalizes super vertex algebra. We develop the bicharacter construction which we use for constructing classes of examples of twisted vertex algebras, as well as for deriving formulas for the operator product expansions, analytic continuations, and normal ordered products. By using the underlying Hopf algebra structure we prove general bicharacter formulas for the vacuum expectation values for two important groups of examples. We show that the correspondences of types B, C, and D-A are isomorphisms of twisted vertex algebras
Boson-fermion mapping and dynamical supersymmetry in fermion models
Navratil, P.; Geyer, H. B.; Dobaczewski, J.
1996-01-01
We show that a dynamical supersymmetry can appear in a purely fermionic system. This ``supersymmetry without bosons" is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In some algebraic fermion models of nuclear structure, particular Hamiltonians may lead to collective spectra of even and odd nuclei that can be unified using the dynamical supersymmetry concept with Pauli correlat...
Coriolis coupling in the interacting boson fermion model
The properties of a boson core coupled to a single-j particle are examined in the framework of the SU(3) limit of the interacting boson fermion model. It is shown that the Coriolis interaction arises in a natural way in this model. Excitation energies are calculated in the large boson number approximation. The analogy to the particle plus rotor model is discussed. (orig.)
It is shown that in a particular basis the dynamical interaction of IBFM for a boson core coupled to a single-j particle in the SU(3) limit takes a tridiagonal form, as does the Coriolis interaction. Interference between this Coriolis-like effect in the boson-fermion dynamical interaction and the genuine Coriolis effect results in interesting features of IBFM: For a particular ratio of the interaction strength, depending only on the angular momentum of the odd particle, the K=j band exactly follows the rotational energy rule, is completely uncoupled from the other bands and has exactly the same moment of inertia as a ground-state band of the core. A possible interpretation of this feature in terms of spectrum-generating supersymmetry is suggested. (orig.)
The Littlewood-Richardson rule and the boson-fermion correspondence
The boson-fermion correspondence is applied to derive explicit formulae for expressing the product of S-functions in terms of sums of S-functions associated to non-standard partitions. (author). Letter-to-the-editor
The structure of 193Au within the Interacting Boson Fermion Model
A γγ angular correlation experiment investigating the nucleus 193Au is presented. In this work the level scheme of 193Au is extended by new level information on spins, multipolarities and newly observed states. The new results are compared with theoretical predictions from a general Interacting Boson Fermion Model (IBFM) calculation for the positive-parity states. The experimental data is in good agreement with an IBFM calculation using all proton orbitals between the shell closures at Z=50 and Z=126. As a dominant contribution of the d3/2 orbital to the wave function of the lowest excited states is observed, a truncated model of the IBFM using a Bose–Fermi symmetry is applied to the describe 193Au. Using the parameters of a fit performed for 193Au, the level scheme of 192Pt, the supersymmetric partner of 193Au, is predicted but shows a too small boson seniority splitting. We obtained a common fit by including states observed in 192Pt. With the new parameters a supersymmetric description of both nuclei is established
Interplay between single-particle and collective features in the boson fermion model
We study the interplay between the single-particle and fermion-pair features in the boson fermion model, both above and below the transition temperature Tc, using the flow equation method. Upon lowering the temperature the single-particle fermionic spectral function (a) gradually develops a depletion of the low-energy states (pseudogap) for T*>T>Tc and a true superconducting gap for Tc and (b) exhibits a considerable transfer of spectral weight between the incoherent background and the narrow coherent peak(s) signifying long-lived quasiparticle features. The Cooperon spectral function consists of a δ-function peak, centered at the renormalized boson energy ω=E-tildeq and a surrounding incoherent background which is spread over a wide energy range. When the temperature approaches Tc from above, this peak for q=0 moves to ω=0, so that the static pair susceptibility diverges (Thouless criterion for the broken symmetry phase transition). Upon decreasing the temperature below Tc the Cooperon peak becomes the collective (Goldstone) mode Eq∝ vertical bar q vertical bar in the small-momentum region and simultaneously splits off from the incoherent background states which are expelled to the high-energy sector vertical bar ω vertical bar ≥2Δsc(T). We discuss the smooth evolution of these features upon approaching Tc from above and consider its feedback on the single-particle spectrum where a gradual formation of damped Bogoliubov modes (above Tc) is observed
The Binding Energy, Spin-Excitation Gap, and Charged Gap in the Boson-Fermion Model
YANG Kai-Hua; TIAN Guang-Shan; HAN Ru-Qi
2003-01-01
In this paper, by applying a simplified version of Lieb 's spin-refleetion-positivity method, which was recentlydeveloped by one of us [G.S. Tian and J.G. Wang, J. Phys. A: Math. Gen. 35 (2002) 941], we investigate some generalproperties of the boson-fermion Hamiltonian, which has been widely used as a phenomenological model to describe thereal-space pairing of electrons. On a mathematically rigorous basis, we prove that for either negative or positive couplingV, which represents the spontaneous decay and recombination process between boson and fermion in the model, thepairing energy of electrons is nonzero. Furthermore, we also show that the spin-excitation gap of the boson-fermionHamiltonian is always larger than its charged gap, as predicted by the pre-paired electron theory.
Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
Wang, Xu-Dong
2016-01-01
In our previous paper we construct a renormalizable Wess-Zumino action on BFNC superspace at the second order approximation of noncommutative parameters. The action contains about 200 terms which are necessary for renormalization. By removing chiral covariant derivatives and chiral coordinates we found that the BFNC Wess-Zumino action can be transformed to a simpler form which have manifest 1/2 supersymmetry. Based on this discovery, we can extend the BFNC Wess-Zumino action to the all order of noncommutative parameters. At first we introduce global symmetries, then obtain divergent operators in the effective action by using dimensional analysis, the next step is to construct all possible BFNC parameters, at the end we combine the BFNC parameters with the divergent operators. We present the explicit action up to the fourth order of noncommutative parameters. Because the action contain all possible divergent operators, it is renormalizable to all order in perturbative theory.
High-Temperature Atomic Superfluidity in Lattice Boson-Fermion Mixtures
Illuminati, F.; Albus, A
2003-01-01
We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always {\\it attractive} if the boson-boson on site interaction is repulsive, and predict the existence of an enhanced BEC--BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion {\\it repulsion}, the induced attraction...
Functional integrals and 1/h expansion in the boson-fermion model
Yan, Jun
2016-06-01
The effective action of boson-fermion model is derived by means of the functional integrals method and Popov-Faddeev canonical transformations. The energy gap equation and excitation spectrum equation are obtained from first order and second order perturbation expansions of functional determinant. In the long wave approximation, some analytical expressions of excitation spectrum are calculated by using the 1/h expansion technique, the results showed that analytical calculation is in good agreement with the numerical calculation. Moreover, the Nambu sum rules of Higgs bosons are analyzed and discussed.
YANG Jin; YU Wan-Lun; XIANG An-Ping
2006-01-01
We use Lewis-Riesenfeld invariant approach to treat the modified Jaynes-Cummings models involving any forms of nonlinearty of the bosonic field when strong boson-fermion couplings are nilpotent Grassmann valued. The general state functions, time evolution operator and the time-evolution expressions for both the bosonic number and the fermionic number are presented.
Level Density In Interacting Boson-Fermion-Fermion Model (IBFFM) Of The Odd-Odd Nucleus 196Au
The level density of the odd-odd nucleus 196Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes.The IBFFM total level density is fitted by Gaussian and its tail is also fitted by Bethe formula and constant temperature Fermi gas model
Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold
Sulkowski, Piotr
2008-01-01
We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural deformations parametrized by a parameter Q: the former one is related to the deformed boson-fermion correspondence introduced by N. Jing, while the latter is the so-called Q-boson, arising also in the context of quantum groups. We show that both deformations are equivalent and can be realized in the same way in the algebra of Hall-Littlewood symmetric functions. Without a deformation, these reduce to Schur functions, which can be used to construct a generating function of plane partitions, reproducing a topological string partition function on $C^3$. A deformation of both systems leads then to a deformed generating function, which reproduces topological string partition function of the conifold, with the deformation parameter Q identified with the size of $P^1$.
Spin-dependent level density in interacting Boson-Fermion-Fermion model of the Odd-Odd Nucleus 196Au
The level density of the odd-odd nucleus 196Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes.The IBFFM spin-dependent level densities show high-spin reduction with respect to Bethe formula.This can be well accounted for by a modified spin-dependent level density formula. (authors)
β -decay rates of Cs-131121 in the microscopic interacting boson-fermion model
Mardones, E.; Barea, J.; Alonso, C. E.; Arias, J. M.
2016-03-01
β -decay rates of Cs-131121 have been calculated in the framework of the neutron-proton interacting boson-fermion model (IBFM-2). For odd-A nuclei, the decay operator can be written in a relatively simple form in terms of the one-nucleon transfer operator. Previous studies of β decay in IBFM-2 were based on a transfer operator obtained by using the number operator approximation (NOA). In this work a new form of the one-nucleon transfer operator, derived microscopically without the NOA approximation, is used. The results from both approaches are compared and show that the deviation from experimental data is reduced without using the NOA approximation. Indications about the renormalization of the Fermi and Gamow-Teller matrix elements are discussed. This is a further step toward a more complete description of low-lying states in medium and heavy nuclei which is necessary to compute reliable matrix elements in studies of current active interest such as double-β decay or neutrino absorption experiments.
A numerical algorithm for modelling boson-fermion stars in dilatonic gravity
We investigate numerically the class of models of the static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem. The first of the parameters is the unknown internal boundary (the radius of the fermionic part of the star) Rs, and the second one represents the frequency Ω of the time oscillations of the boson field. To solve this problem, the whole space [0, ∞) is splitted into two domains: internal [0, Rs] (inside the star) and external [Rs, ∞) (outside the star). In each domain the physical model leads to two nonlinear boundary value problems in respect to metric functions, the functions describing the fermionic and bosonic matter, and the dilaton field. These boundary value problems have different dimensions inside and outside the star, respectively. The solutions in these regions are obtained separately and matched using the necessary algebraic continuity conditions including Rs and Ω. The continuous analogue of the Newton method for solving both the nonlinear differential and algebraic problems is used. The corresponding linearized boundary value problems at each iteration are solved by means of spline-collocation scheme. In this way, we obtain the behaviour of the basic geometric quantities and functions describing a dilaton field and matter fields, which build the star
Salas, P.; Fortes, M.; Solís, M. A.; Sevilla, F. J.
2016-05-01
We adapt the Boson-Fermion superconductivity model to include layered systems such as underdoped cuprate superconductors. These systems are represented by an infinite layered structure containing a mixture of paired and unpaired fermions. The former, which stand for the superconducting carriers, are considered as noninteracting zero spin composite-bosons with a linear energy-momentum dispersion relation in the CuO2 planes where superconduction is predominant, coexisting with the unpaired fermions in a pattern of stacked slabs. The inter-slab, penetrable, infinite planes are generated by a Dirac comb potential, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Composite-bosons condense at a critical temperature at which they exhibit a jump in their specific heat. These two values are assumed to be equal to the superconducting critical temperature Tc and the specific heat jump reported for YBa2Cu3O6.80 to fix our model parameters namely, the plane impenetrability and the fraction of superconducting charge carriers. We then calculate the isochoric and isobaric electronic specific heats for temperatures lower than Tc of both, the composite-bosons and the unpaired fermions, which matches the latest experimental curves. From the latter, we extract the linear coefficient (γn) at Tc, as well as the quadratic (αT2) term for low temperatures. We also calculate the lattice specific heat from the ARPES phonon spectrum, and add it to the electronic part, reproducing the experimental total specific heat at and below Tc within a 5% error range, from which the cubic (ßT3) term for low temperatures is obtained. In addition, we show that this model reproduces the cuprates mass anisotropies.
BEC-polaron gas in a boson-fermion mixture: A many-body extension of Lee-Low-Pines theory
Nakano, Eiji; Yabu, Hiroyuki
2016-05-01
We investigate the ground state properties of the gaseous mixture of a single species of bosons and fermions at zero temperature, where bosons are major in population over fermions, and form the Bose-Einstein condensate (BEC). The boson-boson and boson-fermion interactions are assumed to be weakly repulsive and attractive, respectively, while the fermion-fermion interaction is absent due to the Pauli exclusion for the low energy s -wave scattering. We treat fermions as a gas of polarons dressed with Bogoliubov phonons, which is an elementary excitation of the BEC, and evaluate the ground state properties with the method developed by Lemmens, Devreese, and Brosens (LDB) originally for the electron polaron gas, and also with a general extension of the Lee-Low-Pines theory for many-body systems (eLLP), which incorporates the phonon drag effects as in the original LLP theory. The formulation of eLLP is developed and discussed in the present paper. The binding (interaction) energy of the polaron gas is calculated in these methods and shown to be finite (negative) for the dilute gas of heavy fermions with attractive boson-fermion interactions, though the suppression by the many-body effects exists.
Breaking of de Sitter Symmetry
Bander, Myron
2010-01-01
We show that an interacting spin-0 field on a de Sitter space background will break the underlying de Sitter symmetry. This is done first for a (1+1) de Sitter space where a boson-fermion correspondence permits us to solve certain interacting theories by transforming them into free ones of opposite statistics. A massless boson interacting by a sine-Gordon potential is shown to be equivalent to a free massive fermion with the mass depending on the de Sitter time thus breaking the symmetry explicitly. We then show that for larger dimensions and any boson potential, to one loop, an anomaly develops and the currents generating the de Sitter transformations are not conserved.
Gollwitzer, A.; Hertenberger, R.; Metz, A.; Schiemenz, P.; Valnion, B.D.; Graw, G. [Sektion Physik der Universitaet Muenchen, D-85748 Garching (Germany); Blasi, N.; Lucchini, S.; Micheletti, S.; Pignanelli, M. [Dipartimento di Fisica dellUniversita di Milano, I-20133 Milano (Italy); de Leo, R. [Universita di Bari and Sezione INFN di Bari (Italy); Gill, R.L. [Brookhaven National Laboratory, Upton, New York 11973 (United States); Hategan, C. [Institute of Atomic Physics, Bukarest (Romania); Casten, R.F. [Yale University, A.W. Wright Nuclear Structure Laboratory, New Haven, Connecticut 06520 (United States)
1998-06-01
The {sup 154}Sm({rvec d},t) reaction at high energy resolution (n,{gamma}), average resonance capture (ARC), and coincidence measurements were performed to study the deformed nucleus {sup 153}Sm. Strength distributions from ({rvec d},t) and completeness for I{sup {pi}}= (1) /(2) {sup {minus}} and (3) /(2) {sup {minus}} states up to 1500 keV from ARC provide one of the first detailed tests of the interacting boson fermion model (IBFM) in a deformed nucleus in a multiorbit environment. For negative parity states the model accounts for the large number of low spin ( (1) /(2) {sup {minus}}, (3) /(2) {sup {minus}}) states much better than the Nilsson model since the even-even core in the IBFM calculations automatically includes excited vibrational states. The IBFM calculations also predict (d,t) spectroscopic factors better than the Nilsson model with pairing and Coriolis mixing. Neither the IBFM nor the Nilsson approach can explain the low lying positive parity states. The IBFM calculations show that for certain combinations of parameters, the monopole term in the boson-fermion Hamiltonian has more than a scaling effect: it can attenuate the Coriolis mixing (energy staggering). Finally suggested improvements in the treatment of pairing in the IBFM are made. {copyright} {ital 1998} {ital The American Physical Society}
Several aspect of shape phase transitions and critical point symmetries are reviewed in this contribution within the frameworks of the Interacting Boson Model (IBM) and the Interacting Boson Fermion Model (IBFM) for even and odd systems respectively and compared with collective geometric models. We discuss in particular the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from the spherical limit U(5) to the γ-unstable limit O(6). The spectrum and transition rates at the critical point are similar to those of the even core and they agree qualitatively with the E(5/4) boson-fermion symmetry. We discuss also the UBF (5) to SUBF (3) shape phase transition in which the allowed fermionic orbitals are j = 1/2; 3/2; 5/2. The formalism of the intrinsic or coherent states is used to describe in details the ground state as well as the excited β- and γ- bands. This formalism is also used to calculate the Potential Energy Surface of the cubic quadrupole operator that leads to triaxiality. (author)
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
Frustration and time-reversal symmetry breaking for Fermi and Bose-Fermi systems
Sacha, Krzysztof; Targońska, Katarzyna; Zakrzewski, Jakub
2012-05-01
The modulation of an optical lattice potential that breaks time-reversal symmetry enables the realization of complex tunneling amplitudes in the corresponding tight-binding model. For a superfluid Fermi gas in a triangular lattice potential with complex tunnelings, the pairing function acquires a complex phase, so the frustrated magnetism of fermions can be realized. Bose-Fermi mixtures of bosonic molecules and unbound fermions in the lattice also show interesting behavior. Due to boson-fermion coupling, the fermions become enslaved by the bosons and the corresponding pairing function takes the complex phase determined by the bosons. In the presence of bosons the Fermi system can reveal both gapped and gapless superfluidity.
Boson-fermion stars exploring different configurations
Henriques, A B; Henriques, Alfredo B.; Mendes, Luis E.
2003-01-01
We use the flexibility of the concept of a fermion-boson star to explore different configurations, ranging from objects of atomic size and masses of the order $10^{18}$ g, up to objects of galactic masses and gigantic halos around a smaller core, with possible interesting applications to astrophysics and cosmology, particularly in the context of dark matter.
Symmetries and Symmetry Breaking
Van Oers, W T H
2003-01-01
In understanding the world of matter, the introduction of symmetry principles following experimentation or using the predictive power of symmetry principles to guide experimentation is most profound. The conservation of energy, linear momentum, angular momentum, charge, and CPT involve fundamental symmetries. All other conservation laws are valid within a restricted subspace of the four interactions: the strong, the electromagnetic, the weak, and the gravitational interaction. In this paper comments are made regarding parity violation in hadronic systems, charge symmetry breaking in two nucleon and few nucleon systems, and time-reversal-invariance in hadronic systems.
Complete sets of low-lying 1/2- and 3/2- levels in 185W and 187W have been obtained using measurements of primary γ-rays following average resonance neutron capture at mean incident neutron energies of 2 and 24 keV. The results are discussed in terms of both the Nilsson model and the SU(3) boson-fermion symmetry scheme appropriate to this region. The data highlights the advantages and deficiencies of both frameworks, and shows that neither is able to describe the complete spectrum of low-lying low-spin energy levels. The two approaches are outlined and compared and the role of the missing degrees of freedom in each is discussed. (orig.)
Retarded Boson-Fermion interaction in atomic systems
Sambhu N Datta
2007-09-01
The retarded interaction between an electron and a spin-0 nucleus, that has been derived from electro-dynamical perturbation theory is discussed here. A brief account of the derivation is given. The retarded form is correct through order 2/2. Use of the relative coordinates leads to an effective oneelectron operator that can be used through all orders of perturbation theory. A few unitary transformations give rise to the interaction that is valid in the non-relativistic limit.
Bosons, fermions and anyons in the plane, and supersymmetry
Horvathy, Peter A; Valenzuela, Mauricio
2010-01-01
Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2+1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N=1 and N=2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Levy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inonu-Wigner contrac...
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
We present many varied chiral symmetry models at the quark level which consistently describe strong interaction hadron dynamics. The pattern that emerges is a nonstrange current quark mass scale mcur ≅ (34-69) MeV and a current quark mass ratio (ms/m)cur ≅ 5-6 along with no strange quark content in nucleons. (orig./WL)
LIE SYMMETRIES AND NOETHER SYMMETRIES
PGL Leach
2012-10-01
Full Text Available We demonstrate that so-called nonnoetherian symmetries with which a known first integral is associated of a differential equation derived from a Lagrangian are in fact noetherian. The source of the misunderstanding lies in the nonuniqueness of the Lagrangian.
Symmetry, Symmetry Breaking and Topology
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.
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
Peters, Kirstin
2010-01-01
A well-known result by Palamidessi tells us that {\\pi}mix (the {\\pi}-calculus with mixed choice) is more expressive than {\\pi}sep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla of- fered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of "incestual" processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (ini- tial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result-based on a proper formalization of what it means to break symmetries-without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reason- able encoding from {\\pi}mix i...
CP and other Symmetries of Symmetries
Trautner, Andreas
2016-01-01
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this thesis pioneers the study of outer automorphisms which are not related to C, P, or T. It is shown how outer automorphisms, in general, relate symmetry invariants and, in theories with spontaneous symmetry breaking, imply relations between different vacuum expectation values. Thereby, outer automorphisms can give rise to emergent symmetries. An example model with a discrete symmetry and three copies of the Standard Model ...
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
Chiral symmetry and chiral-symmetry breaking
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
Jaffé, Hans H
1977-01-01
This book, devoted exclusively to symmetry in chemistry and developed in an essentially nonmathematical way, is a must for students and researchers. Topics include symmetry elements and operations, multiple symmetry operations, multiplication tables and point groups, group theory applications, and crystal symmetry. Extensive appendices provide useful tables.
Rasin, A
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Nilles, H. P.; Ratz, M.; Vaudrevange, P. K. S.
2012-01-01
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
Nilles, Hans Peter [Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Bonn Univ. (Germany). Physikalisches Inst.; Ratz, Michael [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-04-15
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
Chiral symmetry and chiral-symmetry breaking
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. (WHK)
Symmetry Analysis of Telegraph Equation
Nadjafikhah, Mehdi; Hejazi, Seyed Reza
2010-01-01
Lie symmetry group method is applied to study the Telegraph equation. 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 symmetries is determined.
Symmetries in subatomic systems
The underlying common themes of the EJC-2010 are symmetries and symmetry violation in relation to nucleon structure, nuclear geometry, isospin and reaction dynamics. The parity violation in electron scattering is the unique probe of strange quarks in nucleons and of neutron skin in heavy nuclei. The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. We also discuss the impact of the symmetries of quantum chromodynamics on the observed properties of hadrons and strongly interacting matter. Mean field approaches are widely used to study nuclear structure properties and correlations between nucleons are treated by symmetry-violating mean field approaches and symmetry properties are currently treated with beyond mean field approaches by using projection techniques. A paper focuses on properties of giant resonances (GR) and particularly on the relationship between GR and isospin symmetry. This document gathers the papers and/or slides of 10 presentations. (A.C.)
Symmetry and symmetry breaking in quantum mechanics
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
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
From physical symmetries to emergent gauge symmetries
Barceló, Carlos; Di Filippo, Francesco; Garay, Luis J
2016-01-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent grav...
van der Schaft, A. J.
1987-01-01
It is argued that the existence of symmetries may simplify, as in classical mechanics, the solution of optimal control problems. A procedure for obtaining symmetries for the optimal Hamiltonian resulting from the Maximum Principle is given; this avoids the actual calculation of the optimal Hamiltonian. This procedure is based upon the notion of symmetry for the Hamiltonian system with inputs and outputs associated with an optimal control problem.
Gray, J E; Vogt, A
1997-01-01
Is symmetry informative? The answer is both yes and no. We examine what information and symmetry are and how they are related. Our approach is primarily mathematical, not because mathematics provides the final word, but because it provides an insightful and relatively precise starting point. Information theory treats transformations that messages undergo from source to destination. Symmetries are information that leave some property of interest unchanged. In this respect the studies of information and symmetry can both be regarded as a Quest for the identity transformation. PMID:9224554
2016-01-01
The Symmetry Festival is a science and art program series, the most important periodic event (see its history) to bring together scientists, artists, educators and practitioners interested in symmetry (its roots, what is behind, applications, etc.), or in the consequences of its absence.
Symmetries of Spectral Problems
Shabat, A.
Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.
Symmetries in Lagrangian Dynamics
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Meshkov, Sydney
2009-01-01
The study of the symmetries of nature has fascinated scientists for eons. The application of the formal mathematical description of symmetries during the last century has produced many breakthroughs in our understanding of the substructure of matter. In this talk, a number of these advances are discussed, and the important role that George Sudarshan played in their development is emphasized
Symmetry relation for helical plasmas: parity symmetry
It is shown that a symmetry relation holds strictly in the LHD (Large Helical Device) type helical magnetic fields. The symmetry relation can be expressed explicitly in the rotating helical coordinate system. It is named as parity symmetry in helical systems. A new concept, - concept of even scalars, odd scalars, even vectors, odd vectors -, is introduced. Calculus of vector operation retains strictly the parity relations for these quantities. For example, the vector product of two vectors with same parity become a odd parity vector. The rotation of a vector field A, ∇ x A, has same parity characteristics with the vector A. It is concluded that the equilibrium magnetic field and current distribution are expressed by even parity vectors. Pressure distribution is expressed by an even parity scalar function. The parity symmetry relations conduct uniquely the power expansion form of equilibrium magnetic field and pressure distribution. Analytical expression for these quantities are obtained approximately by truncation of the power series. Closed magnetic surface, islands, chaotic field line region and divertor field lines are well reproduced by this simple model. (author)
Symmetry Effects in Computation
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
Loebbert, Florian
2016-01-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfeld's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dila...
On the symmetry breaking phenomenon
Birtea, Petre; Puta, Mircea; Ratiu, Tudor S.; Tudoran, Ruazvan Micu
2006-01-01
We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases.
Counting trees using symmetries
Bernardi, Olivier
2012-01-01
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symmetries of refined enumerative formulas: proving these symmetries is easy, and once the symmetries are proved the formulas follow effortlessly. Somewhat surprisingly, our formula for the generating function of multitype Cayley trees appears to be new, and implies certain recent results by Bousquet-M\\'elou and Chapuy. We also adapt our approach to recover known enumerative formulas for cacti counted according to their degree distribution.
Schwichtenberg, Jakob
2015-01-01
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
Symmetry in Boolean Satisfiability
Fadi A. Aloul
2010-06-01
Full Text Available This paper reviews recent approaches on how to accelerate Boolean Satisfiability (SAT search by exploiting symmetries in the problem space. SAT search algorithms traverse an exponentially large search space looking for an assignment that satisfies a set of constraints. The presence of symmetries in the search space induces equivalence classes on the set of truth assignments. The goal is to use symmetries to avoid traversing all assignments by constraining the search to visit a few representative assignments in each equivalence class. This can lead to a significant reduction in search runtime without affecting the completeness of the search.
Sequential flavor symmetry breaking
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
Avery, John Scales; Rettrup, Sten; Avery, James Emil
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding...... such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets...
Symmetry relation for helical plasma. Parity symmetry
It is shown that a strict symmetry relation holds in the LHD (Large Helical Device) type helical magnetic field. The symmetry relation is expressed explicitly in the rotating helical coordinate system and named as parity symmetry in helical system. A new concept, -concept of even scalars, odd scalars, even vectors, odd vectors-, is introduced. Calculus of vector operation retains strictly the parity relations for these quantities. For example, the vector product of two vectors with same parity become an odd parity vector. The rotation of a vector field A, ∇xA, has same parity characteristics with that of the vector A. It is concluded that the equilibrium magnetic field and current distribution are expressed by even parity vectors. Pressure distribution is expressed by an even parity scalar function. The parity symmetry relations conduct uniquely the power expansion form of equilibrium magnetic field and pressure distribution. Analytical expressions for these quantities are obtained approximately by truncation of the power series. An example of vacuum helical magnetic field is shown in the following, B=∇xA+B0(0, 0, r0/r), A=Bp/a=-(p/3r)Y3-(p3/12r3)Y(X4+Y4), -(p/3r)X3-(p3/12r3)X(X4+Y4), -((X2-Y2)/2)(1-(Xcos(pφ)-Ysin(pφ))/4r)-(p4/6r4)X2Y2)=, where p, r0, a, Bp, B0 are constants for magnetic field. Rotating helical coordinate system is expressed by (X, Y, φ) and r≡r0+Xcos (pφ) - Ysin (pφ). Closed magnetic surface, islands, chaotic field line region and divertor field lines are well represented by this simple model. (author)
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
Global Bifurcations With Symmetry
Porter, J B
2001-01-01
Symmetry is a ubiquitous feature of physical systems with profound implications for their dynamics. This thesis investigates the role of symmetry in global bifurcations. In particular, the structure imposed by symmetry can encourage the formation of complex solutions such as heteroclinic cycles and chaotic invariant sets. The first study focuses on the dynamics of 1:n steady-state mode interactions in the presence of O(2) symmetry. The normal form equations considered are relevant to a variety of physical problems including Rayleigh-Bénard convection with periodic boundary conditions. In open regions of parameter space these equations contain structurally stable heteroclinic cycles composed of connections between standing wave, pure mode, and trivial solutions. These structurally stable cycles exist between two global bifurcations, the second of which involves an additional mixed mode state and creates as many as four distinct kinds of structurally unstable heteroclinic cycles. The various cycles c...
Gauge symmetry from decoupling
Wetterich, C
2016-01-01
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.
In the present work, we elucidate the meaning of the custodial symmetry and its importance at the phenomenological level in the framework of the standard model of the electroweak interactions and its possible extensions. (Author)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
Second order symmetry operators
Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac–Weyl equation and the Maxwell equation on a curved four-dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed and used to systematically reduce the equations to a form which allows geometrical interpretation. (paper)
IBM: discrete symmetry viewpoint
It is shown that the set of information of the s and d boson operators which maintain the IBM-like form of the Hamiltonian comprises a discrete point symmetry group D2'. The transformations manifest themselves as a parameter symmetry of the IBM-1 Hamiltonian. The transformations considered are also necessary for constructing the most general IBM-2 Hamiltonian. The properties of the potential energy surfaces arising in connection with these transformations are discussed
IBM: parameter symmetry, hidden symmetries and transformations of boson operators
A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The symmetry is associated with linear canonical transformations of boson operators, or, equivalently, with the existence of different realizations of the symmetry algebras of the models. The relevance of the parameter symmetry to physical observables is discussed. (Author)
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 D4, the other describing quarks and employing the symmetry D14. In the latter model it is the quark mixing matrix element Vud - 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.)
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.)
Regular Symmetry Patterns (Technical Report)
Lin, Anthony W.; Nguyen, Truong Khanh; Rümmer, Philipp; Sun, Jun
2015-01-01
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework for capturing symmetry patterns in parameterised systems (i.e. an infinite family of finite-state systems): two regular word transducers to represent, respectively, parameterised systems and symmetry patterns. The framework subsumes various types of symmetry ...
In unpolarized cross sections constraints imposed by symmetries produce only quantitative changes which, in the absence of the precise knowledge of dynamics, cannot be used to test the validity of those symmetries. In polarization observables, in sharp contrast, imposition of symmetries produces qualitative changes, such as the vanishing of some observables or linear relationships among observables, which can be used to check the validity of symmetries without a detailed knowledge of dynamics. Such polarization observables can also separate the different constraints caused by different symmetries imposed simultaneously. This is illustrated for the two cases when Lorentz invariance and parity conservation, and Lorentz invariance and time reversal invariance, respectively, hold. It is also shown that it is impossible to construct, in any reaction in atomic, nuclear, or particle physics, a null experiment that would unambiguously test the validity of time-reversal invariance independently of dynamical assumptions. Finally, for a general quantum mechanical system undergoing a process, it is shown that one can tell from measurements on this system whether or not the system is characterized by quantum numbers the existence of which is unknown to the observer, even though the detection equipment used by the observer is unable to distinguish among the various possible values of the secret quantum number and hence always averages over them. This allows us to say whether the spin of a particle in a reaction is zero or not even if they can measure nothing about that particle's polarization. 5 references
Baldo, M
2016-01-01
The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry ene...
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang–Mills theory in four dimensions.
Yi-Nan, Fang; Guo-Hui, Dong; Duan-Lu, Zhou; Chang-Pu, Sun
2016-04-01
Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry (DoS) as a non-negative continuous number ranging from zero to unity. DoS is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G, and thus is computable by making use of the completeness relations of the irreducible representations of G. The monotonicity of DoS can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some (spontaneous) symmetry breaking. Supported by the National Natural Science Foundation of China under Grant Nos. 11421063, 11534002, 11475254 and the National 973 Program under Grant Nos. 2014CB921403, 2012CB922104, and 2014CB921202
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs
Binary Tetrahedral Flavor Symmetry
Eby, David A
2013-01-01
A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibb...
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...
Hidden Symmetry Subgroup Problems
Decker, Thomas; Santha, Miklos; Wocjan, Pawel
2011-01-01
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden Subgroup Problem (HSP). Given a group acting on a set and an oracle whose level sets define a partition of the set, the task is to recover the subgroup of symmetries of this partition inside the group. The HSSP provides a unifying framework that, besides the HSP, encompasses a wide range of algebraic oracle problems, including quadratic hidden polynomial problems. While the HSSP can have provably exponential quantum query complexity, we obtain efficient quantum algorithms for various interesting cases. To achieve this, we present a general method for reducing the HSSP to the HSP, which works efficiently in several cases related to symmetries of polynomials. The HSSP therefore connects in a rather surprising way certain hidden polynomial problems with the HSP. Using this connect...
Beyond-mean-field boson-fermion model for odd-mass nuclei
Nomura, K.; Nikšić, T.; Vretenar, D.
2016-05-01
A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.
Beyond mean-field boson-fermion model for odd-mass nuclei
Nomura, K; Vretenar, D
2016-01-01
A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.
Formation of Singlet Fermion Pairs in the Dilute Gas of Boson-Fermion Mixture
Samoilov V.
2010-10-01
Full Text Available We argue the formation of a free neutron spinless pairs in a liquid helium -dilute neutron gas mixture. We show that the term, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. Due to presented theoretical approach, we prove that the electron pairs in superconductivity could be discovered by Froelich earlier then it was made by the Cooper.
Free expansion of fermionic dark solitons in a boson-fermion mixture
We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a 'notch' in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion
Formation of Singlet Fermion Pairs in the Dilute Gas of Boson-Fermion Mixture
Minasyan V.
2010-10-01
Full Text Available We argue the formation of a free neutron spinless pairs in a liquid helium -dilute neutron gas mixture. We show that the term, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. Due to presented theoretical approach, we prove that the electron pairs in superconductivity could be discovered by Frölich earlier then it was made by the Cooper.
de Vega, H. J.; Medrano, M. Ramon; Sanchez, N.
1992-07-01
We investigate the physical implications and particle content of superstring scattering in the supergravity shock-wave background recently found by us. The amplitudes for the different particle transmutation processes taking place in this geometry are explicitly computed for Gree-Schwarz superstring, including the new phenomena of fermion to boson and boson to fermion transmutations. Transition amplitudes among the ground states, first and second excited states are obtained. Particularly interesting are the amplitudes within the massless particle sector, which lead to physical massive particles upon supersymmetry breaking at low energies.
Observed supersymmetry in baryon and meson spectra with IBFM, the interacting boson fermion model
Supersymetry is already observed in (i) nuclear physics where the same empirical formula based on a graded Lie group describles even-even and odd-even nuclear spectra and (ii) in Nambu-BCS theory where there is a simple relationship between the energy gap of the basic fermion and the bosonic collective modes. Similar relationships between large number of mesonic and baryonic excitations based on the SU(3) substructure in the U(15/30) graded Lie group, are proposed. (author)
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Foot, R; Volkas, R R
1992-01-01
Quark-lepton symmetric models are a class of gauge theories motivated by the similarities between the quarks and leptons. In these models the gauge group of the standard model is extended to include a ``color'' group for the leptons. Consequently, the quarks and leptons can then be related by a $Z_2$ discrete quark-lepton symmetry which is spontaneously broken by the vacuum. Models utilizing quark-lepton symmetry with acceptable and interesting collider phenomenology have been constructed. The cosmological consequences of these models are also discussed.
Arzano, Michele
2016-01-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter kappa to be derived via precision measurements of discrete symmetries and CPT.
Liu, Keh-Fei
2016-01-01
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $\\pi N \\sigma$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
Measures with symmetry properties
Schindler, Werner
2003-01-01
Symmetries and invariance principles play an important role in various branches of mathematics. This book deals with measures having weak symmetry properties. Even mild conditions ensure that all invariant Borel measures on a second countable locally compact space can be expressed as images of specific product measures under a fixed mapping. The results derived in this book are interesting for their own and, moreover, a number of carefully investigated examples underline and illustrate their usefulness and applicability for integration problems, stochastic simulations and statistical applications.
We review the current status of heavy-quark symmetry and its applications to weak decays of hadrons containing a single heavy quark. After an introduction to the underlying physical ideas, we discuss in detail the formalism of the heavy-quark effective theory, including a comprehensive treatment of symmetry breaking corrections. We then illustrate some nonperturbative approaches, which aim at a dynamical, QCD-based calculation of the universal form factors of the effective theory. The main focus is on results obtained using QCD sum rules. Finally, we perform an essentially model-independent analysis of semileptonic B meson decays in the context of the heavy-quark effective theory. ((orig.))
The vanishing of the one-loop string cosmological constant in nontrivial nonsupersymmetric backgrounds can be understood by viewing the path integral as an inner product of orthogonal wave functions. For special backgrounds the string theory has an extra symmetry, expressed as a transformation on moduli space. When left- and right-moving wave functions transform in different representations of this symmetry the cosmological constant must vanish. Specific examples of the mechanism are given at one loop for theories in two and four dimensions. Various suggestions are made for the higher loop extension of this idea. (orig.)
Weakly broken galileon symmetry
Pirtskhalava, David [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); Santoni, Luca; Trincherini, Enrico [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); INFN, Sezione di Pisa, Piazza dei Cavalieri 7, 56126 Pisa (Italy); Vernizzi, Filippo [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, Gif-sur-Yvette cédex, F-91191 (France)
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Introduction to chiral symmetry
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented
Clader, Emily
2014-01-01
These expository notes are based on lectures by Yongbin Ruan during a special semester on the B-model at the University of Michigan in Winter 2014. They outline and compare the mirror symmetry constructions of Batyrev-Borisov, Hori-Vafa, and Bergland-Hubsch-Krawitz.
Fields, symmetries, and quarks
'Fields, symmetries, and quarks' covers elements of quantum field theory, symmetries, gauge field theories and phenomenological descriptions of hadrons, with special emphasis on topics relevant to nuclear physics. It is aimed at nuclear physicists in general and at scientists who need a working knowledge of field theory, symmetry principles of elementary particles and their interactions and the quark structure of hadrons. The book starts out with an elementary introduction into classical field theory and its quantization. As gauge field theories require a working knowledge of global symmetries in field theories this topic is then discussed in detail. The following part is concerned with the general structure of gauge field theories and contains a thorough discussion of the still less widely known features of Non-Abelian gauge field theories. Quantum Chromodynamics (QCD), which is important for the understanding of hadronic matter, is discussed in the next section together with the quark compositions of hadrons. The last two chapters give a detailed discussion of phenomenological bag-models. The MIT bag is discussed, so that all theoretical calculations can be followed step by step. Since in all other bag-models the calculational methods and steps are essentially identical, this chapter should enable the reader to actually perform such calculations unaided. A last chapter finally discusses the topological bag-models which have become quite popular over the last few years. (orig.)
Gray, P L
2003-01-01
"The subatomic pion particle breaks the charge symmetry rule that governs both fusion and decay. In experiments performed at the Indiana University Cyclotron Laboratory, physicists forced heavy hydrogen (1 proton + 1 neutron) to fuse into helium in a controlled, measurable environment" (1 paragraph).
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also underst...
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also unders...
Gauging without Initial Symmetry
Kotov, Alexei
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued 1-form gauge fields so as to lift the symmetry to Maps(Sigma,G). Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields v_a on the target M satisfying the extended Killing equation v_{a(i;j)}=0 for some connection acting on the index a. For regular foliations this is equivalent to merely requiring the distribution orthogonal to the leaves to be invariant with respect to leaf...
Gauging without initial symmetry
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Σ, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(Σ , G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / ∼. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
On Symmetries in Optimal Control
van der Schaft, A. J.
1986-01-01
We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.
Dynamical symmetry and shape coexistence
A general discussion is given of extending the Fermion Dynamical Symmetry Model to describe shape coexistence. The theory is applied to the description of superdeformation and normal deformations through alternative dynamical symmetries
Discrete Symmetries CP, T, CPT
Bernabeu, J
2016-01-01
The role of Symmetry Breaking mechanisms to search for New Physics is of highest importance. We discuss the status and prospects of the Discrete Symmetries CP, T, CPT looking for their separate Violation in LHC experiments and meson factories.
Symmetry and topology in evolution
This volume contains papers of an interdisciplinary symposium on evolution. The aim of this symposium, held in Budapest, Hungary, 28-29 May 1991, was to clear the role of symmetry and topology at different levels of the evolutionary processes. 21 papers were presented, their topics included evolution of the Universe, symmetry of elementary particles, asymmetry of the Earth, symmetry and asymmetry of biomolecules, symmetry and topology of lining objects, human asymmetry etc. (R.P.)
Concurrent symmetries: the interplay between local and global molecular symmetries.
Echeverría, Jorge; Carreras, Abel; Casanova, David; Alemany, Pere; Alvarez, Santiago
2011-01-01
We analyze in this article the degree to which different groups of atoms retain local symmetries when assembled in a molecule. This study is carried out by applying continuous symmetry measures to several families of mixed sandwiches, a variety of piano-stool molecules, and several organic groups. An analysis of the local symmetry of the electron density shows that, sandwiched between two regions of different symmetry that correspond to the ligand sets, its symmetry is cylindrical at the central metal atom. PMID:21207632
Charge independence and charge symmetry
Miller, G A; Miller, Gerald A; van Oers, Willem T H
1994-01-01
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed.
Dynamical Symmetries in Classical Mechanics
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
Charge independence and charge symmetry
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed. (author). 145 refs., 3 tabs., 11 figs
The Geometry of Noncommutative Symmetries
We discuss the notion of noncommutative symmetries based on Hopf algebras in the geometric models constructed within the framework of non-commutative geometry. We introduce and discuss several notions of non-commutative symmetries and outline the construction specific examples, for instance, finite algebras and the application of symmetries in the derivation of the Dirac operator for the noncommutative torus. (author)
Emergence of Symmetries from Entanglement
CERN. Geneva
2016-01-01
Maximal Entanglement appears to be a key ingredient for the emergence of symmetries. We first illustrate this phenomenon using two examples: the emergence of conformal symmetry in condensed matter systems and the relation of tensor networks to holography. We further present a Principle of Maximal Entanglement that seems to dictate to a large extend the structure of gauge symmetry.
Asymmetry, Symmetry and Beauty
Abbe R. Kopra
2010-07-01
Full Text Available Asymmetry and symmetry coexist in natural and human processes. The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion and symmetric opposition (sinusoidal waves are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition. These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series. The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.
Conformal symmetries of spacetimes
In this paper, we give a unified and global new approach to the study of the conformal structure of the three classical Riemannian spaces as well as of the six relativistic and non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, and both Newton-Hooke and Galilean). We obtain general expressions within a Cayley-Klein framework, holding simultaneously for all these nine spaces, whose cycles (including geodesics and circles) are explicitly characterized in a new way. The corresponding cycle-preserving symmetries, which give rise to (Moebius-like) conformal Lie algebras, together with their differential realizations are then deduced without having to resort to solving the conformal Killing equations. We show that each set of three spaces with the same signature type and any curvature have isomorphic conformal algebras; these are related through an apparently new conformal duality. Laplace and wave-type differential equations with conformal algebra symmetry are finally constructed. (author)
A broken symmetry ontology: Quantum mechanics as a broken symmetry
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
Herrero, O F, E-mail: o.f.herrero@hotmail.co [Conservatorio Superior de Musica ' Eduardo Martinez Torner' Corrada del Obispo s/n 33003 - Oviedo - Asturias (Spain)
2010-06-01
Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.
Cluster Symmetries and Dynamics
Freer Martin
2016-01-01
Full Text Available Many light nuclei display behaviour that indicates that rather than behaving as an A-body systems, the protons and neutrons condense into clusters. The α-particle is the most obvious example of such clustering. This contribution examines the role of such α-clustering on the structure, symmetries and dynamics of the nuclei 8Be, 12C and 16O, recent experimental measurements and future perspectives.
Fabella, Raul V.
1997-01-01
We consider teams where information asymmetry (adverse selection and moral hazard) is minimized by entry point screening designed to produce homogenous membership and work group arrangements and job rotation that render effort at worst imperfectly observable. We show that under membership symmetry, budget balance and strict rationality, a self-enforcing Pareto efficient (cooperates) and envy-free solution is attainable if and only production technology is of a unique concave family. Even in t...
Dynamical Electroweak Symmetry Breaking
Hošek, Jiří; Smetana, Adam
Berlin: Springer, 2014, s. 17-28. ISBN 978-3-319-07072-8 R&D Projects: GA ČR GA202/06/0734; GA MŠk LA08015; GA MŠk LA08032 Institutional support: RVO:61389005 Keywords : dynamical electroweak symmetry breaking * top-quark condensation * neutriono condensation * strong Yukawa dynamics * flavor gauge dynamics Subject RIV: BE - Theoretical Physics
Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.
Christodoulides, Demetrios
2015-03-01
Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.
This new edition of Prof. Strocchi's well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit in terms of the delocalized Coulomb dynamics. Furthermore, the chapter on the Higgs mechanism has been significantly expanded with a non-perturbative treatment of the Higgs phenomenon, at the basis of the standard model of particle physics, in the local and in the Coulomb gauges. Last but not least, a subject index has been added and a number of misprints have been corrected. From the reviews of the first edition: The notion of spontaneous symmetry breaking has proven extremely valuable, the problem is that most derivations are perturbative and heuristic. Yet mathematically precise versions do exist, but are not widely known. It is precisely the aim of his book to correct this unbalance. - It is remarkable to see how much material can actually be presented in a rigorous way (incidentally, many of the results presented are due to Strocchi himself), yet this is largely ignored, the original heuristic derivations being, as a rule, more popular. - At each step he strongly emphasizes the physical meaning and motivation of the various notions introduced, a book that fills a conspicuous gap in the literature, and does it rather well. It could also be a good basis for a graduate course in mathematical physics. It can be recommended to physicists as well and, of course, for physics/mathematics libraries. J.-P. Antoine, Physicalia 28/2, 2006 Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the non-symmetric ground states and the infinite extension of the system. It is written in a pleasant style at a level suitable for graduate students in
Vladan Nikolić
2015-02-01
Full Text Available The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D and 3D perception analyses. We start analyzing a pair of twin buildings with projection of the architectural composition elements in 2D picture plane (plane of the composition and we distinguish four 2D keyframe cases based on the relation between the bilateral symmetry of the twin composition and the bilateral symmetry of each element. In 3D perception for each 2D keyframe case there are two sub-variants, with and without a symmetry plane parallel to the picture plane. The bilateral symmetry is dominant if the corresponding symmetry plane is orthogonal to the picture plane. The essence of the complete classification is relation between the bilateral (dominant symmetry of the architectural composition and the bilateral symmetry of each element of that composition.
Rotational-isotopic symmetries
In this note we submit a nonlocal (integral) generalization of the rotational-isotopic symmetries O-circumflex(3) introduced in preceding works for nonlinear and nonhamiltonian systems in local approximation. By recalling that the Lie-isotopic theory naturally admits nonlocal terms when all embedded in the isounit, while the conventional symplectic geometry is strictly local-differential, we introduce the notion of symplectic-isotopic two-forms, which are exact symplectic two-forms admitting a factorization into the Kronecker product of a canonical two-form time the isotopic element of an underlying Euclidean-isotopic space. Topological consistency is then achieved by embedding all nonlocal terms in the isounit of the iso-cotangent bundle, while keeping the local topology for the canonical part. In this way, we identify the symplectic-isotopic geometry as being the natural geometrical counterpart of the Lie-isotopic theory. The results are used for the introduction of the notion of Birkhoffian angular momentum, that is, the generalization of the conventional canonical angular momentum which is applicable to Birkhoffian systems with generally nonlinear, nonlocal and nonhamiltonian internal forces. The generators J (and the parameters θ) coincide with the conventional quantities. Nevertheless, the quantity J is defined on the underlying Euclidean-isotopic space, by therefore acquiring a generalized magnitude. The isocommutation rules and isoexponentiation of the Birkhoffian angular momentum are explicitly computed and shown to characterize the most general known nonlinear and nonlocal realization of the isorotational symmetry. The local isomorphisms between the infinitely possible isotopes O-circumflex(3) and the conventional symmetry O(3) is proved. Finally the isosymmetries O-circumflex(3) are used to characterize the conserved, total, Birkhoffian angular momentum of closed nonselfadjoint systems. (author). 4 refs
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
Conformal Symmetry and Unification
Pawlowski, M
1998-01-01
The Weyl-Weinberg-Salam model is presented. It is based on the local conformal gauge symmetry. The model identifies the Higgs scalar field in SM with the Penrose-Chernikov-Tagirov scalar field of the conformal theory of gravity. Higgs mechanism for generation of particle masses is replaced by the originated in Weyl's ideas conformal gauge scale fixing. Scalar field is no longer a dynamical field of the model and does not lead to quantum particle-like excitations that could be observed in HE experiments. Cosmological constant is naturally generated by the scalar quadric term. The model admits Weyl vector bosons that can mix with photon and weak bosons.
Baldo, M.; Burgio, G.F.
2016-01-01
The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symme...
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
Kubo, Jisuke [Kanazawa Univ., Inst. for Theoretical Physics, Kanazawa (Japan); Mondragon, Alfonso; Mondragon, Myriam; Rodriguez-jauregui, Ezequiel [UNAM, Instituto de Fisica, Mexico (Mexico)
2003-05-01
Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S{sub 3}, we suggest a minimal S{sub 3} invariant extension of the standard model. We find that in the leptonic sector, the exact S{sub 3} x Z{sub 2} symmetry, which allows 6 real independent parameters, is consistent with experimental data and predicts the bi-maximal mixing of the left-handed neutrinos and that the third neutrino is the lightest neutrino. Z{sub 2} is anomaly-free, but it forbids CP-violations in the leptonic, as well as in the hadronic sector. Therefore, the origin of CP-violations can be identified with the breaking of the Z{sub 2} symmetry, which may be understood in a more fundamental theory. With the exact S{sub 3} only, there are 10 real independent parameters and one independent phase, on which the Cabibbo-Kobayashi-Maskawa mixing matrix V{sub CKM} depends. A set of values of these parameters that are consistent with experimental observations is given. (author)
Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S3, we suggest a minimal S3 invariant extension of the standard model. We find that in the leptonic sector, the exact S3 x Z2 symmetry, which allows 6 real independent parameters, is consistent with experimental data and predicts the bi-maximal mixing of the left-handed neutrinos and that the third neutrino is the lightest neutrino. Z2 is anomaly-free, but it forbids CP-violations in the leptonic, as well as in the hadronic sector. Therefore, the origin of CP-violations can be identified with the breaking of the Z2 symmetry, which may be understood in a more fundamental theory. With the exact S3 only, there are 10 real independent parameters and one independent phase, on which the Cabibbo-Kobayashi-Maskawa mixing matrix VCKM depends. A set of values of these parameters that are consistent with experimental observations is given. (author)
Kubo, J; Mondragón, M N; Rodríguez-Jáuregui, E
2003-01-01
Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S_3, we suggest a minimal S_3 invariant extension of the standard model. We find that in the leptonic sector the exact S_3 X Z_2 symmetry, which allows 6 real independent parameters, is consistent with experimental data and predicts the bi-maximal mixing of the left-handed neutrinos and that the $tau$ neutrino is the lightest neutrinno. Z_2 is anomaly-free, but forbids CP-violations in the leptonic as well as in the hadronic sector. Therefore, we may identify the origin of the CP-violations with the breaking of the Z_2 symmetry, which may be understood in a more fundamental theory. With the exact S_3 only, there are 10 real independent parameters and one independent phase in the hadronic sector. A set of the values of these parameters that are consistent with the experimental observations is given.
Applications of chiral symmetry
The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature Tχ implies that the ρ and a1 vector mesons are degenerate in mass. In a gauged linear sigma model the ρ mass increases with temperature, mρ(Tχ) > mρ(0). The author conjectures that at Tχ the thermal ρ - a1, peak is relatively high, at about ∼1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The ω meson also increases in mass, nearly degenerate with the ρ, but its width grows dramatically with temperature, increasing to at least ∼100 MeV by Tχ. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from open-quotes quenchedclose quotes heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates
Bootstrap Dynamical Symmetry Breaking
Wei-Shu Hou
2013-01-01
Full Text Available Despite the emergence of a 125 GeV Higgs-like particle at the LHC, we explore the possibility of dynamical electroweak symmetry breaking by strong Yukawa coupling of very heavy new chiral quarks Q . Taking the 125 GeV object to be a dilaton with suppressed couplings, we note that the Goldstone bosons G exist as longitudinal modes V L of the weak bosons and would couple to Q with Yukawa coupling λ Q . With m Q ≳ 700 GeV from LHC, the strong λ Q ≳ 4 could lead to deeply bound Q Q ¯ states. We postulate that the leading “collapsed state,” the color-singlet (heavy isotriplet, pseudoscalar Q Q ¯ meson π 1 , is G itself, and a gap equation without Higgs is constructed. Dynamical symmetry breaking is affected via strong λ Q , generating m Q while self-consistently justifying treating G as massless in the loop, hence, “bootstrap,” Solving such a gap equation, we find that m Q should be several TeV, or λ Q ≳ 4 π , and would become much heavier if there is a light Higgs boson. For such heavy chiral quarks, we find analogy with the π − N system, by which we conjecture the possible annihilation phenomena of Q Q ¯ → n V L with high multiplicity, the search of which might be aided by Yukawa-bound Q Q ¯ resonances.
Angel Garrido
2011-01-01
Full Text Available In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.
SYMMETRY IN WORLD TRADE NETWORK
Hui WANG; Guangle YAN; Yanghua XIAO
2009-01-01
Symmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network (WTN) has been rarely studied so far. In this paper, the authors systematically explore the symmetry in WTN. The authors construct WTN in 2005 and explore the size and structure of its automorphism group, through which the authors find that WTN is symmetric, particularly, locally symmetric to a certain degree. Furthermore, the authors work out the symmetric motifs of WTN and investigate the structure and function of the symmetric motifs, coming to the conclusion that local symmetry will have great effect on the stability of the WTN and that continuous symmetry-breakings will generate complexity and diversity of the trade network. Finally, utilizing the local symmetry of the network, the authors work out the quotient of WTN, which is the structural skeleton dominating stability and evolution of WTN.
Symmetry of crystals and molecules
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.
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).
Trieste lectures on mirror symmetry
These are pedagogical lectures on mirror symmetry given at the Spring School in ICTP, Trieste, March 2002. The focus is placed on worldsheet descriptions of the physics related to mirror symmetry. We start with the introduction to general aspects of (2,2) supersymmetric field theories in 1 + 1 dimensions. We next move on to the study and applications of linear sigma model. Finally, we provide a proof of mirror symmetry in a class of models. (author)
Quarks, baryons and chiral symmetry
Hosaka, Atsushi
2001-01-01
This book describes baryon models constructed from quarks, mesons and chiral symmetry. The role of chiral symmetry and of quark model structure with SU(6) spin-flavor symmetry are discussed in detail, starting from a pedagogic introduction. Emphasis is placed on symmetry aspects of the theories. As an application, the chiral bag model is studied for nucleon structure, where important methods of theoretical physics, mostly related to the semiclassical approach for a system of strong interactions, are demonstrated. The text is more practical than formal; tools and ideas are explained in detail w
The conservation of orbital symmetry
Woodward, R B
2013-01-01
The Conservation of Orbital Symmetry examines the principle of conservation of orbital symmetry and its use. The central content of the principle was that reactions occur readily when there is congruence between orbital symmetry characteristics of reactants and products, and only with difficulty when that congruence does not obtain-or to put it more succinctly, orbital symmetry is conserved in concerted reaction. This principle is expected to endure, whatever the language in which it may be couched, or whatever greater precision may be developed in its application and extension. The book ope
Physical Theories with Average Symmetry
Alamino, Roberto C
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violations of physical symmetries, as for instance Lorentz invariance in some quantum gravity theories, is briefly commented.
An introduction to Yangian symmetries
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
Symmetries of Quantum Nonsymmetric Gravity
Mebarki, N; Boudine, A; Benslama, A
1999-01-01
Symmetries of Quantum Nonsymmetric gravity are studied and the corresponding generators are constructed . The related equal time canonical (and non canonical) (anti) commutation relations are established.
Segmentation Using Symmetry Deviation
Hollensen, Christian; Højgaard, L.; Specht, L.;
2011-01-01
the 10 hypopharyngeal cancer patients to find anatomical symmetry and evaluate it against the standard deviation of the normal patients to locate pathologic volumes. Combining the information with an absolute PET threshold of 3 Standard uptake value (SUV) a volume was automatically delineated. The...... overlap of automated segmentations on manual contours was evaluated using concordance index and sensitivity for the hypopharyngeal patients. The resulting concordance index and sensitivity was compared with the result of using a threshold of 3 SUV using a paired t-test. Results: The anatomical and...... overlap concordance index and sensitivity of respectively 0.43±0.15 and 0.56±0.18 was acquired. It was compared to the concordance index of segmentation using absolute threshold of 3 SUV giving respectively 0.41±0.16 and 0.51±0.19 for concordance index and sensitivity yielding p-values of 0.33 and 0...
Lie Symmetries of Ishimori Equation
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Symmetry violation in nuclear reactions
Precision studies of nuclear reactions can be used to search for small violations of the discrete symmetries. Recent and proposed experimental work using nuclear reactions to study the breakdown of three symmetries - isospin (I), parity (P) and time-reversal (T) is reviewed. 44 references
Behind the shirts, is symmetry
Galam, S
1998-01-01
The outbreak of spontaneous order in matter results from symmetry breaking. How does a system change its collective organisation ? How does it break its own symmetry ? That are the questions which are answered using a metaphoric world of shirts and colors.
BRST symmetry of Unimodular Gravity
Upadhyay, S.; Oksanen, M.; Bufalo, R.
2015-01-01
We derive the BRST symmetry for two versions of unimodular gravity, namely, fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant. The BRST symmetry is generalized further to the finite field-dependent BRST, in order to establish the connection between different gauges in each of the two versions of unimodular gravity.
Generalized Atkin-Lehner symmetry
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner ''selection rule'' approach for obtaining a vanishing one-loop cosmological constant
Shape analysis with subspace symmetries
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).
Symmetry inheritance of scalar fields
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Symmetry inheritance of scalar fields
Smolić, Ivica
2015-01-01
Matter fields don't necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to Komar mass and angular momentum of the black hole scalar hair.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Asymptotic symmetries from finite boxes
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Discrete symmetries in the MSSM
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.)
UV completion without symmetry restoration
Endlich, Solomon; Penco, Riccardo
2013-01-01
We show that it is not possible to UV-complete certain low-energy effective theories with spontaneously broken space-time symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform non-linearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of space-time and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
FANGJian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
Symmetries in nuclear structure
Allaart, K; Dieperink, A
1983-01-01
The 1982 summer school on nuclear physics, organized by the Nuclear Physics Division of the Netherlands' Physical Society, was the fifth in a series that started in 1963. The number of students attending has always been about one hundred, coming from about thirty countries. The theme of this year's school was symmetry in nuclear physics. This book covers the material presented by the enthusi astic speakers, who were invited to lecture on this subject. We think they have succeeded in presenting us with clear and thorough introductory talks at graduate or higher level. The time schedule of the school and the location allowed the participants to make many informal contacts during many social activities, ranging from billiards to surf board sailing. We hope and expect that the combination of a relaxed atmosphere during part of the time and hard work during most of the time, has furthered the interest in, and understanding of, nuclear physics. The organization of the summer school was made possible by substantia...
Gravitation and Gauge Symmetries
Stewart, J
2002-01-01
The purpose of this book (I quote verbatim from the back cover) is to 'shed light upon the intrinsic structure of gravity and the principle of gauge invariance, which may lead to a consistent unified field theory', a very laudable aim. The content divides fairly clearly into four sections (and origins). After a brief introduction, chapters 2-6 review the 'Structure of gravity as a theory based on spacetime gauge symmetries'. This is fairly straightforward material, apparently based on a one-semester graduate course taught at the University of Belgrade for about two decades, and, by implication, this is a reasonably accurate description of its level and assumed knowledge. There follow two chapters of new material entitled 'Gravity in flat spacetime' and 'Nonlinear effects in gravity'. The final three chapters, entitled 'Supersymmetry and supergravity', 'Kaluza-Klein theory' and 'String theory' have been used for the basis of a one-semester graduate course on the unification of fundamental interactions. The boo...
The suggestion by Jaffe that if σ is a light q2q-bar2 state 0++ then even the fundamental chiral transformation properties of the σ becomes unclear, has stimulated much interest. Adler pointed out that in fact the seminal work on chiral symmetry via PCAC consistency, is really quite consistent with the σ being predominantly q2q-bar2. This interpretation was actually backed by subsequent work on effective Lagrangian methods for linear and non linear realizations. More recent work of Achasov suggests that intermediate four-quark states determine amplitudes involving other scalars a0(980) and f0(980) below 1 GeV, and the report by Ning Wu that study on σ meson in J/ψ → ωπ+π- continue to support a non qq-bar σ with mass as low as 390 MeV. It is also noted that more recent re-analysis of πK scattering by S. Ishida et al. together with the work of the E791 Collaboration, support the existence of the scalar κ particle with comparatively light mass as well
On Discrete Gauge Symmetries in Trinification Model
Laamara, R Ahl; Ennadifi, S -E; Nassiri, S
2016-01-01
Given the important role of discrete gauge symmetries in viable models, we discuss these symmetries in intersecting D6-brane trinification model where the ZN symmetry is investigated and its identification is shown.
Symmetry protected single photon subradiance
Cai, Han; Svidzinsky, Anatoly A; Zhu, Shi-Yao; Scully, Marlan O
2016-01-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shift cannot be neglected. We find that anti-symmetric states are subradiant states for distribution with reflection symmetry. These states can be prepared by anti-symmetric optical modes and converted to superradiant states by properly tailored 2\\pipulses. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
$PT$ Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
Mannheim, Philip D.
2014-01-01
We present some interesting connections between $PT$ symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be $PT$ symmetric, with it being $iA_{\\mu}$ rather than $A_{\\mu}$ itself that then appears in the connection. With this modification the standard minimal coupl...
OPTICAL METAMATERIALS WITH QUASICRYSTALLINE SYMMETRY: SYMMETRY-INDUCED OPTICAL ISOTROPY
Kruk, Sergey S.; Decker, Manuel; Helgert, Christian
2013-01-01
We compare, both experimentally and theoretically, metamaterials with three different symmetries: square lattice, hexagonal lattice, and quasicrystalline Penrose tiling. By relying on an advanced Jones calculus, we link the symmetry properties to the farfield optical response, such as ellipticity and circular dichroism, as the incident angle is varied. We show that hexagonal lattice metamaterials, when compared to the square ones, exhibit less circular dichroism and ellipticity due t...
Symmetry violations in subatomic physics
This book presents papers on chiral symmetry, phase transitions, QCD lattices and sum rules, QCD reactions and deep inelastic processes, and electroweak interactions. The papers include gluon interactions and proton scattering and the chiral bag model with vector mesons
Kohn's theorem and Galilean symmetry
Zhang, P-M
2011-01-01
The relation between the separability of a system of charged particles in a uniform magnetic field and Galilean symmetry is revisited using Duval's "Bargmann framework". If the charge-to-mass ratios of the particles are identical, $e_a/m_a=\\epsilon$ for all particles, then the Bargmann space of the magnetic system is isometric to that of an anisotropic harmonic oscillator. Assuming that the particles interact through a potential which only depends on their relative distances, the system splits into one representing the center of mass plus a decoupled internal part, and can be mapped further into an isolated system using Niederer's transformation. Conversely, the manifest Galilean boost symmetry of the isolated system can be "imported" to the oscillator and to the magnetic systems, respectively, to yield the symmetry used by Gibbons and Pope to prove the separability. For vanishing interaction potential the isolated system is free and our procedure endows all our systems with a hidden Schroedinger symmetry, au...
Relativistic Symmetry and Entangled Correlations
Kellman, M E
2002-01-01
It is argued that the standard quantum mechanical description of the Bell correlations between entangled subsystems is in conflict with relativistic space-time symmetry. Proposals to abandon relativistic symmetry, in the sense of explicitly returning to an absolute time and preferred frame, are rejected on the grounds that the preferred frame is not empirically detectable, so the asymmetry is an unsatisfactory feature in physical theory. A "symmetric view" is proposed in which measurement events on space-like separated entangled subsystems are connected by a symmetric two-way mutual influence. Because of this reciprocity, there is complete symmetry of the description: Einsteinian relativity of simultaneity and space-time symmetry are completely preserved. The nature of the two-way influence is considered, as well as the possibility of an empirical test.
External symmetry in general relativity
We propose a generalization of the isometry transformations to the geometric context of the spin field theories where the local frames are explicitly involved. We define the external symmetry transformations as isometries combined with suitable tetrad gauge transformations and we show that these form a group which is locally isomorphic with the isometry one. We point out that the symmetry transformations leave invariant the field equations and have generators with specific spin terms that represent new physical observables. The examples we give are the generators of the central symmetry and those of the maximal symmetries of the de Sitter and anti-de Sitter spacetimes for which we derive the spin terms in different tetrad gauge fixings. (author)
Symmetry and quaternionic integrable systems
Gaeta, G.; Rodríguez, M. A.
2015-01-01
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so-called hyperHamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperHamiltonian systems, i.e. quaternionic oscillators, and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperHamiltonian systems.
Hidden Symmetries in Simple Graphs
Allen D. Parks
2012-03-01
Full Text Available It is shown that each element s in the normalizer of the automorphism group Aut(G of a simple graph G with labeled vertex set V is an Aut(G invariant isomorphism between G and the graph obtained from G by the s permutation of V—i.e., s is a hidden permutation symmetry of G. A simple example illustrates the theory and the applied notion of system robustness for reconfiguration under symmetry constraint (RUSC is introduced.
Conformal symmetry in quantum finance
The quantum finance symmetries are studied. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited and the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed. In addition, it is shown that the operators of this last representation are not hermitian and not conserved.
Dynamical symmetries in nuclear structure
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs
Flavored Peccei-Quinn symmetry
Ahn, Y H
2014-01-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a $\\mu$--$\\tau$ power law in the lepton sector, such that relatively large 13 mixing angle with bi-large ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong CP problem, in a way that no domain wall problem occurs, based on $A_{4}\\times U(1)_{X}$ symmetry in a supersymmetric framework. Here we refer to the global $U(1)_X$ symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry". In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under $U(1)_X$, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected each other. So, the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around $10^{12}$ GeV se...
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
FANG Jian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable masssystem are studied. Thedefinitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system aregiven. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Meisymmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
Symmetry and symmetry breaking. Symetrie et brisure de symetrie
Balian, R. (CEA/Saclay, Direction des Sciences de la Matiere (DSM), 91 - Gif-sur-Yvette (France)); Lambert, D. (Facultes Universitaires Notre-Dame de la Paix, Namur (Belgium)); Brack, A. (Centre National de la Recherche Scientifique (CNRS), 45 - Orleans-la-Source (France). Centre de Biophysique Moleculaire); Englert, F. (Universite Libre de Bruxelles (Belgium). Laboratoire de Physique Theorique)
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.) 103 refs.
Symmetry and symmetry breaking; Symetrie et brisure de symetrie
Balian, R. [CEA/Saclay, Direction des Sciences de la Matiere (DSM), 91 - Gif-sur-Yvette (France); Lambert, D. [Facultes Universitaires Notre-Dame de la Paix, Namur (Belgium); Brack, A. [Centre National de la Recherche Scientifique (CNRS), 45 - Orleans-la-Source (France). Centre de Biophysique Moleculaire; Englert, F. [Universite Libre de Bruxelles (Belgium). Laboratoire de Physique Theorique; Chomaz, Ph. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France); Lachieze-Rey, M. [CEA/Saclay, Dept. d`Astrophysique, de la Physique des Particules, de la Physique Nucleaire et de l`Instrumentation Associee (DAPNIA), 91 - Gif-sur-Yvette (France); Emery, E. [Ecole Polytechnique Federale, Lausanne (Switzerland); Cohen-Tannoudji, G.; Sacquin, Y
1999-11-01
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.) 103 refs.
Geometric aspects of some hidden symmetries
Hidden symmetries of two dimensional chiral models are analysed from the geometric point of view. The dual symmetry gives rise to generalized isometries of the metric on the space of dependent variables. The Jacobi equation of geodesic deviation is dual invariant and the generalized isometries lead to generalized symmetries of the field equations. Being variational divergence symmetries they generate families of conservation laws. (orig.)
Symmetry and group theory in chemistry
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
O'Hanlon actions by Noether symmetry
Darabi, F
2015-01-01
By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials respecting Noether symmetry in O'Hanlon action in Einstein frame.
Novel Symmetries in Christ-Lee Model
Kumar, R
2015-01-01
We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turn out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties.
Interfacial Fermi Loops from Interfacial Symmetries
Takahashi, Ryuji; Murakami, Shuichi
2014-01-01
We propose a concept of interfacial symmetries such as interfacial particle-hole symmetry and interfacial time-reversal symmetry, which appear in interfaces between two regions related to each other by particle-hole or time-reversal transformations. These symmetries result in novel dispersion of interface states. In particular for the interfacial particle-hole symmetry the gap closes along a loop ("Fermi loop") at the interface. We numerically demonstrate this for the Fu-Kane-Mele tight-bindi...
Miller, G A
2003-01-01
Two new experiments have detected charge-symmetry breaking, the mechanism responsible for protons and neutrons having different masses. Symmetry is a crucial concept in the theories that describe the subatomic world because it has an intimate connection with the laws of conservation. The theory of the strong interaction between quarks - quantum chromodynamics - is approximately invariant under what is called charge symmetry. In other words, if we swap an up quark for a down quark, then the strong interaction will look almost the same. This symmetry is related to the concept of sup i sospin sup , and is not the same as charge conjugation (in which a particle is replaced by its antiparticle). Charge symmetry is broken by the competition between two different effects. The first is the small difference in mass between up and down quarks, which is about 200 times less than the mass of the proton. The second is their different electric charges. The up quark has a charge of +2/3 in units of the proton charge, while ...
An Introduction to Emergent Symmetries
Gomes, Pedro R S
2015-01-01
These are intended to be introductory notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some elementary background material and proceed to our discussion by examining several interesting problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.
Hidden Symmetries of Stochastic Models
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.
Soft theorems from anomalous symmetries
Huang, Yu-tin
2015-01-01
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the alpha' expansion of string theory amplitudes, we study the matrix elements of operator R^4 with half maximal supersymmetry. We construct the non-linear completion of R^4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R^4.
Symmetry Breaking in Finite Volume
LIU Chuan
2000-01-01
Spontaneous symmetry breaking is a cooperative phenomenon for systems with infinitely many degrees of freedom and it plays an essential role in quantum field theories. Lattice O(N) model is studied within the Hamiltonian approach using an adiabatic approximation. It is shown that the low-lying spectrum of the system in the broken phase can be understood by using the adiabatic, or Born-Oppenheimer approximation, which turns out to become an expansion in the inverse power of volume. In the infinite volume limit, the symmetry is broken while in the finite volume the slow rotation of the zero-momentum mode restores the symmetry and gives rise to the rotator spectrum, which has been observed in realistic Monte Carlo simulations.
Symmetry breaking in molecular ferroelectrics.
Shi, Ping-Ping; Tang, Yuan-Yuan; Li, Peng-Fei; Liao, Wei-Qiang; Wang, Zhong-Xia; Ye, Qiong; Xiong, Ren-Gen
2016-07-11
Ferroelectrics are inseparable from symmetry breaking. Accompanying the paraelectric-to-ferroelectric phase transition, the paraelectric phase adopting one of the 32 crystallographic point groups is broken into subgroups belonging to one of the 10 ferroelectric point groups, i.e. C1, C2, C1h, C2v, C4, C4v, C3, C3v, C6 and C6v. The symmetry breaking is captured by the order parameter known as spontaneous polarization, whose switching under an external electric field results in a typical ferroelectric hysteresis loop. In addition, the responses of spontaneous polarization to other external excitations are related to a number of physical effects such as second-harmonic generation, piezoelectricity, pyroelectricity and dielectric properties. Based on these, this review summarizes recent developments in molecular ferroelectrics since 2011 and focuses on the relationship between symmetry breaking and ferroelectricity, offering ideas for exploring high-performance molecular ferroelectrics. PMID:27051889
Heisenberg symmetry and hypermultiplet manifolds
Antoniadis, Ignatios; Petropoulos, P Marios; Siampos, Konstantinos
2015-01-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.
Symmetries in nuclei and molecules
Recent progress in two different fronts is reported. First, the concept of bisection of a harmonic oscillator or hydrogen atom, used in the past in establishing the connection between U(3) and O(4), is generalized into multisection (trisection, tetra section, etc.). It is then shown that all symmetries of the N-dimensional anisotropic harmonic oscillator with rational ratios of frequencies (RHO), some of which are underlying the structure of superdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry of the corresponding isotropic oscillator with the appropriate combination of multisections. Furthermore, it is seen that bisections of the N-dimensional hydrogen atom, which possesses an O(N+1) symmetry, lead to the U(N) symmetry, so that further multisections of the hydrogen atom lead to the symmetries of the N-dim RHO. The opposite is in general not true, i.e. multisections of U(N) do not lead to O(N+1) symmetries, the only exception being the occurrence of O(4) after the bisection of U(3). Second, it is shown that there is evidence that the recently observed in superdeformed nuclear bands δ I=4 bifurcation is also occurring in normal deformed bands of actinides and rare earths, in hyperdeformed nuclear bands, as well as in rotational bands of diatomic molecules. In addition there is evidence that a δ I=8 bifurcation, of the same order of magnitude as the δ I=4 one, is observed in superdeformed nuclear bands and rotational bands of diatomic molecules. (author)
Chiral symmetry on the lattice
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model
Local symmetry in random graphs
Simões, Jefferson Elbert; Figueiredo, Daniel R.; Barbosa, Valmir C.
2016-01-01
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their automorphism groups, which do not account for the similarity of local structures. We introduce the concept of local symmetry, which reflects the structural equivalence of the vertices' egonets. We study the emergence of asymmetry in the Erd\\H{o}s-R\\'enyi rand...
Renormalizable models with broken symmetries
The results of the renormalized perturbation theory, in the absence of massless quanta, are summarized. The global symmetry breaking is studied and the associated currents are discussed in terms of the coupling with a classical Yang Mills field. Gauge theories are discussed; it is most likely that the natural set up should be the theory of fiber bundles and that making a choice of field coordinates makes the situation obscure. An attempt is made in view of clarifying the meaning of the Slavnov symmetry which characterizes gauge field theories
Symmetry of intramolecular quantum dynamics
Burenin, Alexander V
2012-01-01
The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigorous in the sense that their correctness is limited only to the correct choice of symmetry of the internal dynamics. The book is basically intended for scientists working in the field of molecular spectroscopy, quantum and structural chemistry.
Spontaneous symmetry breaking in QCD
We study dynamical chiral symmetry breaking in QCD by the use of the generalized Hartree-Fock method. The low energy quark mass is calculated to the second order of diagrammatic expansion around shifted perturbative vacuum where quarks are massive. We show that the low energy mass is finite and renormalization group invariant. We find that the finite mass gap emerges as the solutions of gap equation and stationarity condition, thereby breaking the chiral symmetry. We also discuss the possibility that the breaking solution may exist up to all orders. (author)
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Spontaneous violation of mirror symmetry
Dyatlov, Igor T
2015-01-01
A symmetry violation model is considered for a system that can spontaneously choose between identical states which differ from each other only in weak properties (R-L). Such mirror symmetry allows reproduction of observed qualitative properties of quark and lepton mixing matrices. The lepton mixing matrix evidences in this case in favor of the inverse mass spectrum and the Dirac nature of SM neutrino. Notwithstanding the Dirac properties of neutrino, an exchange of lepton numbers such as $e^{-}+\\mu^{+}\\rightarrow e^{+}+\\mu^{-}$ is possible but with only leptons participating in the process.
Symposium Symmetries in Science XIII
Gruber, Bruno J; Yoshinaga, Naotaka; Symmetries in Science XI
2005-01-01
This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.
Clifford algebraic symmetries in physics
This paper reviews the following appearances of Clifford algebras in theoretical physics: statistical mechanics; general relativity; quantum electrodynamics; internal symmetries; the vee product; classical electrodynamics; charged-particle motion; and the Lorentz group. It is concluded that the power of the Clifford-algebraic description resides in its ability to perform representation-free calculations which are generalizations of the traditional vector algebra and that this considerable computational asset, in combination with the intrinsic symmetry, provides a practical framework for much of theoretical physics. 5 references
Optical metamaterials with quasicrystalline symmetry: symmetry-induced optical isotropy
Taking advantage of symmetry considerations, we have analyzed the potential of various metamaterials to affect the polarization state of light upon oblique illumination. We have shown that depending on the angle of illumination, metamaterials are able to support specific polarization states. The presented methodology that using ellipticity and circular dichroism, provides an unambiguous language for discussing the impact of the inherent symmetry of the metamaterial lattices on their far-field response. Our findings allow the quantification analysis of the impact of inter-element coupling and lattice symmetry on the optical properties of metamaterials, and to separate this contribution from the response associated with a single meta-atom. In addition, we have studied the concept of optical quasicrystalline metamaterials, revealing that the absence of translational symmetry (periodicity) of quasicrystalline metamaterials causes an isotropic optical response, while the long-range positional order preserves the resonance properties. Our findings constitute an important step towards the design of optically isotropic metamaterials and metasurfaces. (authors)
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
A model of intrinsic symmetry breaking
Ge, Li [Research Center for Quantum Manipulation, Department of Physics, Fudan University, Shanghai 200433 (China); Li, Sheng [Department of Physics, Zhejiang Normal University, Zhejiang 310004 (China); George, Thomas F., E-mail: tfgeorge@umsl.edu [Office of the Chancellor and Center for Nanoscience, Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, MO 63121 (United States); Department of Physics and Astronomy, University of Missouri-St. Louis, St. Louis, MO 63121 (United States); Sun, Xin, E-mail: xin_sun@fudan.edu.cn [Research Center for Quantum Manipulation, Department of Physics, Fudan University, Shanghai 200433 (China)
2013-11-01
Different from the symmetry breaking associated with a phase transition, which occurs when the controlling parameter is manipulated across a critical point, the symmetry breaking presented in this Letter does not need parameter manipulation. Instead, the system itself suddenly undergoes symmetry breaking at a certain time during its evolution, which is intrinsic symmetry breaking. Through a polymer model, it is revealed that the origin of the intrinsic symmetry breaking is nonlinearity, which produces instability at the instance when the evolution crosses an inflexion point, where this instability breaks the original symmetry.
Diffeomorphism symmetry in quantum gravity models
Dittrich, Bianca
2008-01-01
We review and discuss the role of diffeomorphism symmetry in quantum gravity models. Such models often involve a discretization of the space-time manifold as a regularization method. Generically this leads to a breaking of the symmetries to approximate ones, however there are incidences in which the symmetries are exactly preserved. Both kind of symmetries have to be taken into account in covariant and canonical theories in order to ensure the correct continuum limit. We will sketch how to identify exact and approximate symmetries in the action and how to define a corresponding canonical theory in which such symmetries are reflected as exact and approximate constraints.
Chiral symmetry in perturbative QCD
The chiral symmetry of quantum chromodynamics with massless quarks is unbroken in perturbation theory. Dimensional regularization is used. The ratio of the vector and axial vector renormalization constante is shown to be independent of the renormalization mass. The general results are explicitly verified to fourth order in g, the QCD coupling constant
Strong coupling electroweak symmetry breaking
Barklow, T.L. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Burdman, G. [Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics; Chivukula, R.S. [Boston Univ., MA (United States). Dept. of Physics
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Quantitative Analysis of Face Symmetry.
Tamir, Abraham
2015-06-01
The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait. PMID:26080172
Fundamental Symmetries and Conservation Laws
I discuss recent progress in low-energy tests of symmetries and conservation laws, including parity nonconservation in atoms and nuclei, electric dipole moment tests of time-reversal invariance, β-decay correlation studies, and decays violating separate (family) and total lepton number.
Instantons and chiral symmetry breaking
A detailed investigation of chiral symmetry breaking due to instanton dynamics is carried out, within the framework of the dilute gas approximation, for quarks in both the fundamental and adjoint representations of SU(2). The momentum dependence of the dynamical mass is found to be very similar in each representation. (orig.)
Turning Students into Symmetry Detectives
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
Experimental tests of fundamental symmetries
Jungmann, K. P.
2014-01-01
Ongoing experiments and projects to test our understanding of fundamental inter- actions and symmetries in nature have progressed significantly in the past few years. At high energies the long searched for Higgs boson has been found; tests of gravity for antimatter have come closer to reality; Loren
Symmetry structure and phase transitions
Ashok Goyal; Meenu Dahiya; Deepak Chandra
2003-05-01
We study chiral symmetry structure at ﬁnite density and temperature in the presence of external magnetic ﬁeld and gravity, a situation relevant in the early Universe and in the core of compact stars. We then investigate the dynamical evolution of phase transition in the expanding early Universe and possible formation of quark nuggets and their survival.
Superdeformations and fermion dynamical symmetries
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU3 of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU3 fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU3 symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting γ-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs
Hidden Local Symmetry and Beyond
Yamawaki, Koichi
2016-01-01
Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H= SU(2)_L x SU(2)_R/SU(2)_V with additional symmetry, the nonlinearly realized scale symmetry. Then the SM does have a dynamical gauge boson of the SU(2)_V HLS, "SM rho meson", in addition to the Higgs as a pseudo dilaton as well as the NG bosons to be absorbed into the W and Z. Based on the recent work done with S. Matsuzaki and H. Ohki, I discuss a novel possibility that the SM rho meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call "Dark SM skyrmi...
Quantum group and quantum symmetry
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
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
Mannheim, Philip D.
2016-05-01
We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
Noether gauge symmetry approach in quintom cosmology
Aslam, Adnan; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-01-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether Gauge Symmetries (NGS). Motivated by this mathematical tool, in this article, we discuss the generalized Noether symmetry of Quintom model of dark energy, which is a two component fluid model of quintessence and phantom fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potentia...
Site symmetry and crystal symmetry: a spherical tensor analysis
Brouder, Christian; Juhin, Amélie; Bordage, Amélie; Arrio, Marie-Anne
2008-01-01
27 pages, 3 figures International audience The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-r...
Feshbach resonances and weakly bound molecular states of boson-boson and boson-fermion NaK pairs
Viel, Alexandra; Simoni, Andrea
2016-01-01
We study theoretically magnetically induced Feshbach resonances and near-threshold bound states in isotopic NaK pairs. Our calculations accurately reproduce Feshbach spectroscopy data on Na$^{40}$K and explain the origin of the observed multiplets in the p-wave [Phys. Rev. A 85, 051602(R) (2012)]. We apply the model to predict scattering and bound state threshold properties of the boson-boson Na$^{39}$K and Na$^{41}$K systems. We find that the Na$^{39}$K isotopic pair presents broad magnetic ...
Feshbach resonances and weakly bound molecular states of boson-boson and boson-fermion NaK pairs
Viel, Alexandra; Simoni, Andrea
2016-04-01
We conduct a theoretical study of magnetically induced Feshbach resonances and near-threshold bound states in isotopic NaK pairs. Our calculations accurately reproduce Feshbach spectroscopy data on Na 40K and explain the origin of the observed multiplets in the p wave [Phys. Rev. A 85, 051602(R) (2012), 10.1103/PhysRevA.85.051602]. We apply the model to predict scattering and bound state threshold properties of the boson-boson Na 39K and Na 41K systems. We find that the Na 39K isotopic pair presents broad magnetic Feshbach resonances and favorable ground-state features for producing nonreactive polar molecules by two-photon association. Broad s -wave resonances are also predicted for Na 41K collisions.
On the definition of cylindrical symmetry
Carot, J.; Senovilla, J. M. M.; Vera, R
1999-01-01
The standard definition of cylindrical symmetry in General Relativity is reviewed. Taking the view that axial symmetry is an essential pre-requisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped, this leading to a new, more general definition of cylindrical symmetry. Stationarity and staticity in cylindrically symmetric spacetimes are then defined, and these issues are analysed in connection with orthogonal trans...
Yet another symmetry breaking to be discovered
Yoshimura, M
2016-01-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in the low energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to search for this class of symmetry breaking, the lepton number violation linked to generation of the matter-antimatter asymmetry in our universe.
Symmetry energy in nuclear density functional theory
W. Nazarewicz; Reinhard, P. -G.; Satula, W.; Vretenar, D.
2013-01-01
The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using...
Yet another symmetry breaking to be discovered
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Symmetry Breaking for Black-Scholes Equations
YANG Xuan-Liu; ZHANG Shun-Li; QU Chang-Zheng
2007-01-01
Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.
Symmetry Breaking for Black-Scholes Equations
Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng
2007-06-01
Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.
Symmetry Breaking for Black-Scholes Equations
Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.
Symmetry and electromagnetism. Simetria y electromagnetismo
Fuentes Cobas, L.E.; Font Hernandez, R.
1993-01-01
An analytical treatment of electrostatic and magnetostatic field symmetry, as a function of charge and current distribution symmetry, is proposed. The Newmann Principle, related to the cause-effect symmetry relation, is presented and applied to the characterization of simple configurations. (Author) 5 refs.
Relativistic dissipative hydrodynamics with spontaneous symmetry breaking
Pujol, C
2003-01-01
In this paper we consider dissipative hydrodynamic equations for systems with continuous broken symmetries. We first present the case of superfluidity, in which the symmetry U(1) is broken and then generalize to the chiral symmetry $SU(2)_L \\times SU(2)_R$. New transport coefficients are introduced and the consequences of their existence are discussed.
Symmetries of the dissipative Hofstadter model
Freed, D E
1993-01-01
The dissipative Hofstadter model, which describes a particle in 2-D subject to a periodic potential, uniform magnetic field, and dissipation, is also related to open string boundary states. This model exhibits an SL(2,Z) duality symmetry and hidden reparametrization invariance symmetries. These symmetries are useful for finding exact solutions for correlation functions.
Symmetry study of the coupled Burgers system
Lian Zengju [Department of Physics, Ningbo University, Ningbo 315211 (China); Lou, S.Y. [Department of Physics, Ningbo University, Ningbo 315211 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)
2006-01-01
The inverse of the recursion operator of a coupled Burgers equation is given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and it's inverse on the trivial symmetries, space translation, identity transformation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra.
Symmetry study of the coupled Burgers system
The inverse of the recursion operator of a coupled Burgers equation is given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and it's inverse on the trivial symmetries, space translation, identity transformation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra
General Formalism for the BRST Symmetry
Abstract In this paper we will discuss Faddeev—Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory. (physics of elementary particles and fields)
Electroweak symmetry breaking at photon colliders
The electroweak-symmetry-breaking sector of the standard model can be weakly-coupled or can be strongly-coupled, which is characterized by some kinds of strong interaction among the Goldstone bosons of the electroweak-symmetry-breaking sector. In this paper, we summarize an investigation of probing the strong electroweak-symmetry-breaking effects at photon colliders. ((orig.))
Dark Matter and Global Symmetries
Mambrini, Yann; Queiroz, Farinaldo S
2015-01-01
General considerations in general relativity and quantum mechanics rule out global symmetries in the context of any consistent theory of quantum gravity. Motivated by this, we derive stringent and robust bounds from gamma-ray, X-ray, cosmic ray, neutrino and CMB data on models that invoke global symmetries to stabilize the dark matter particle. Under realistic assumptions we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime. We then specialize our analysis and apply our bounds to specific models such as the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. In the supplemental material we derive robust, updated model-independent limits on the dark matter lifetime.