Axial gravity, massless fermions and trace anomalies

International Nuclear Information System (INIS)

Bonora, L.; Cvitan, M.; Giaccari, S.; Stemberga, T.; Prester, P.D.; Pereira, A.D.; UFF-Univ. Federal Fluminense, Niteroi

2017-01-01

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)

Axial gravity, massless fermions and trace anomalies

Energy Technology Data Exchange (ETDEWEB)

Bonora, L. [International School for Advanced Studies (SISSA), Trieste (Italy); KEK, Tsukuba (Japan). KEK Theory Center; INFN, Sezione di Trieste (Italy); Cvitan, M.; Giaccari, S.; Stemberga, T. [Zagreb Univ. (Croatia). Dept. of Physics; Prester, P.D. [Rijeka Univ. (Croatia). Dept. of Physics; Pereira, A.D. [UERJ-Univ. Estadual do Rio de Janeiro (Brazil). Dept. de Fisica Teorica; UFF-Univ. Federal Fluminense, Niteroi (Brazil). Inst. de Fisica

2017-08-15

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)

Algebraic and computational aspects of real tensor ranks

CERN Document Server

Sakata, Toshio; Miyazaki, Mitsuhiro

2016-01-01

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...

Chiral fermions on the lattice

International Nuclear Information System (INIS)

Randjbar Daemi, S.; Strathdee, J.

1995-01-01

The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi-flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in D dimensions and show that they coincide with the bilinear part of the effective action of D-dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2-dimensional gravitation and Maxwell fields. (author). 15 refs

Dynamic origins of fermionic D -terms

Science.gov (United States)

Hudson, Jonathan; Schweitzer, Peter

2018-03-01

The D -term is defined through matrix elements of the energy-momentum tensor, similarly to mass and spin, yet this important particle property is experimentally not known any fermion. In this work we show that the D -term of a spin 1/2 fermion is of dynamical origin: it vanishes for a free fermion. This is in pronounced contrast to the bosonic case where already a free spin-0 boson has a non-zero intrinsic D -term. We illustrate in two simple models how interactions generate the D -term of a fermion with an internal structure, the nucleon. All known matter is composed of elementary fermions. This indicates the importance to study this interesting particle property in more detail, which will provide novel insights especially on the structure of the nucleon.

Worldline path integrals for fermions with general couplings

International Nuclear Information System (INIS)

D'Hoker, E.; Gagne, D.G.

1996-01-01

We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance. (orig.)

Spinors, tensors and the covariant form of Dirac's equation

International Nuclear Information System (INIS)

Chen, W.Q.; Cook, A.H.

1986-01-01

The relations between tensors and spinors are used to establish the form of the covariant derivative of a spinor, making use of the fact that certain bilinear combinations of spinors are vectors. The covariant forms of Dirac's equation are thus obtained and examples in specific coordinate systems are displayed. (author)

On heterotic vacua with fermionic expectation values

Energy Technology Data Exchange (ETDEWEB)

Minasian, Ruben [Institut de Physique Theorique, Universite Paris Saclay, CEA, CNRS, Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Universites, CNRS, LPTHE, UPMC Paris 06, UMR 7589, Paris (France); Svanes, Eirik Eik [Sorbonne Universites, CNRS, LPTHE, UPMC Paris 06, UMR 7589, Paris (France); Sorbonne Universites, Institut Lagrange de Paris, Paris (France)

2017-03-15

We study heterotic backgrounds with non-trivial H-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear Σ{sub MNP} = tr anti χΓ{sub MNP}χ. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form Σ{sub mnp} that must be a singlet of the holonomy group. This condition does not hold anymore when an internal H-flux is turned on and O(α{sup '}) effects are included. In this paper we study flux compactifications to three and four-dimensions on G-structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Bosonization of fermions coupled to topologically massive gravity

Science.gov (United States)

Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.

2014-03-01

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space-time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space-time.

Bosonization of fermions coupled to topologically massive gravity

International Nuclear Information System (INIS)

Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.

2014-01-01

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space–time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy–momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space–time.

Bosonization of fermions coupled to topologically massive gravity

Energy Technology Data Exchange (ETDEWEB)

Fradkin, Eduardo [Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080 (United States); Moreno, Enrique F. [Department of Physics, Northeastern University, Boston, MA 02115 (United States); Schaposnik, Fidel A. [Departamento de Física, Universidad Nacional de La Plata, Instituto de Física La Plata, C.C. 67, 1900 La Plata (Argentina)

2014-03-07

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space–time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy–momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space–time.

Fermion boson metamorphosis in field theory

International Nuclear Information System (INIS)

Ha, Y.K.

1982-01-01

In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered

Itinerant quantum multicriticality of two-dimensional Dirac fermions

Science.gov (United States)

Roy, Bitan; Goswami, Pallab; Juričić, Vladimir

2018-05-01

We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions (d =2 ) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break O(S1) and O(S2) symmetries in the ordered phase. Performing a renormalization-group analysis by using the ɛ =(3 -d ) expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged O(S1+S2) chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either O(S1) or O(S2) chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.

Vector and tensor meson production in quasi-two-body final states using the dual fermion model

International Nuclear Information System (INIS)

Becker, L.; Matthaeus, E.; Weigt, G.

1976-01-01

Phenomenological dual fermion amplitudes are obtained by using Neveu-Schwarz-Ramond model as a guide to incorporate half-integer spin. The model relates the production mechanism of different resonances lying on the same degenerate Regge trajectory, thus allowing a simultaneous description of vector and tensor meson production. A characteristic feature of the amplitudes is their non-evasive coupling structure. Predictions of the model for rho 0 -f-g 0 , ω-A 2 - and anti K*(890)-anti K*(1420) production in quasi-two-body reactions are compared with experimental data. The differential cross sections for natural and unnatural spin-parity t-channel exchanges as well as their contributions to different helicities of the produced resonances are given. In particular, new properties arise from the non-evasive pion exchange. Reasonable agreement with the data is found. (Auth.)

Vector and tensor meson production in quasi-two-body final states using the dual fermion model

International Nuclear Information System (INIS)

Becker, L.; Matthaeus, E.; Weigt, G.

1975-01-01

Phenomenological dual fermion amplitudes are obtained by using the Neveu-Schwarz-Ramond model as a guide to incorporate half-integer spin. The model relates the production mechanism of different resonances lying on the same degenerated Regge trajectory, thus allowing a simultaneous description of vector and tensor meson production. A characteristic feature of the amplitudes is their non-evasive coupling structure. Predictions of the model for rho 0 - f - g 0 , ω - A 2 - and anti K-890 and anti K-1420 resonances production in quasi-two-body reactions are compared with experimental data. The differential cross sections for natural and unnatural spin-parity t-channel exchanges as well as their contributions to different helicities of the produced resonances are given. In particular, new properties arise from the non-evasive pion exchange. Reasonable agreement with the data is found. (author)

Vacuum polarization and chiral lattice fermions

International Nuclear Information System (INIS)

Randjbar Daemi, S.; Strathdee, J.

1995-09-01

The vacuum polarization due to chiral fermions on a 4-dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge invariant regularization of the fermion vacuum amplitude. Its low energy - long wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan-Symanzik, RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson-type mass parameters. (author). 16 refs

Generators of the exceptional group E8 as bilinear quark and lepton fields

International Nuclear Information System (INIS)

Koca, M.

1981-01-01

The quarks and leptons are assigned to the adjoint representation of the exceptional group E 8 using decompositions under the subgroups SU(9) and [SU(3)] 4 . Generators are constructed as linear combinations of bilinear quark and lepton fields. Closure of the algebra is used to determine the unknown coefficients of the linear combinations. It is noted that the Majorana spinors chi/sup μ//sub ν/ introduced to represent the adjoint representations of SU(9) and [SU(3)] 4 subgroups cannot be taken traceless. The trace chi/sup μ//sub ν/ should couple to the quark and lepton fields in order to close the algebra. The constraints on the bilinear fields which are of physical importance are introduced to obtain the right number of fermionic states in the adjoint representation. An attractive possibility of having an octet of strictly massless Majorana quarks and at least three massless Majorana leptons as a consequence of pure algebraic constraints is discussed. The exceptional subgroups E 7 and E 6 are identified and the explicit commutation relations are obtained. Using one assignment of E 6 the role of color-singlet lepton-lepton and quark-antiquark currents is pointed out

Tensor Network Wavefunctions for Topological Phases

Science.gov (United States)

Ware, Brayden Alexander

intrinsically fermionic topological phases, i.e. topological phases contructed out of fermions with a nontrivial response to fermion parity defects. A zero correlation length wavefunction and a commuting projector Hamiltonian that realizes this wavefunction as its ground state are constructed. Using an appropriate generalization of the minimally entangled states method for extraction of topological order from the ground states on a torus to the intrinsically fermionic case, we fully characterize the corresponding topological order as Ising x (px - ipy). We argue that this phase can be captured using fermionic tensor networks, expanding the applicability of tensor network methods.

Bilinear effect in complex systems

Science.gov (United States)

Lam, Lui; Bellavia, David C.; Han, Xiao-Pu; Alston Liu, Chih-Hui; Shu, Chang-Qing; Wei, Zhengjin; Zhou, Tao; Zhu, Jichen

2010-09-01

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. The bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.

Lefschetz thimbles in fermionic effective models with repulsive vector-field

Science.gov (United States)

Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira

2018-06-01

We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion bilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. This "auxiliary" sign problem can be solved by using the Lefschetz-thimble path-integral method, where the integration path is constructed in the complex plane. Another serious obstacle in the numerical construction of Lefschetz thimbles is caused by singular points and cuts induced by multivalued functions of the complexified scalar field in the momentum integration. We propose a new prescription which fixes gradient flow trajectories on the same Riemann sheet in the flow evolution by performing the momentum integration in the complex domain.

Fermionic zero-norm states and enlarged supersymmetries of Type II string

International Nuclear Information System (INIS)

Lee, J.-C.

2000-01-01

We calculate the NS-R fermionic zero-norm states of the type II string spectrum. The massless and some possible massive zero-norm states are seen to be responsible for the space-time supersymmetry. The existence of other fermionic massive zero-norm states with higher spinor-tensor indices correspond to new enlarged boson-fermion symmetries of the theory at high energy. We also discuss the R-R charges and R-R zero-norm states and justify the idea that the perturbative string does not carry the massless R-R charges. (orig.)

Abelian tensor models on the lattice

Science.gov (United States)

Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi

2018-04-01

We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.

Thermofield dynamics and Casimir effect for fermions

International Nuclear Information System (INIS)

Queiroz, H.; Silva, J.C. da; Khanna, F.C.; Malbouisson, J.M.C.; Revzen, M.; Santana, A.E.

2005-01-01

A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons [Phys. Rev. A 66 (2002) 052101], and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a three-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons

Coleman-Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field II: the fermion spectrum

Science.gov (United States)

Adler, Stephen L.

2017-07-01

We continue our study of Coleman-Weinberg symmetry breaking induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler 2014 Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We focus in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for giving the spin \\frac{3}{2} field a mass by the BEH mechanism, and analyze the remaining massless spin \\frac{1}{2} fermions, the global chiral symmetries, and the running couplings after symmetry breaking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1) B-L , and conjecture that the theory runs to an infrared fixed point at which there is a massless gluon with 3 to  -1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric breaking of Sp(4) to SU(2) subgroups, one of which is the electroweak SU(2), and the other of which is a ‘technicolor’ group that binds the original SU(8) model fermions, which play the role of ‘preons’, into composites. Quarks can emerge as 5 preon composites and leptons as 3 preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

Quantum corrections in thermal states of fermions on anti-de Sitter space-time

Science.gov (United States)

Ambruş, Victor E.; Winstanley, Elizabeth

2017-12-01

We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.

The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant

Energy Technology Data Exchange (ETDEWEB)

Ito, Yuta [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Graduate University for Advanced Studies (SOKENDAI),1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)

2016-12-05

In many interesting physical systems, the determinant which appears from integrating out fermions becomes complex, and its phase plays a crucial role in the determination of the vacuum. An example of this is QCD at low temperature and high density, where various exotic fermion condensates are conjectured to form. Another example is the Euclidean version of the type IIB matrix model for 10d superstring theory, where spontaneous breaking of the SO(10) rotational symmetry down to SO(4) is expected to occur. When one applies the complex Langevin method to these systems, one encounters the singular-drift problem associated with the appearance of nearly zero eigenvalues of the Dirac operator. Here we propose to avoid this problem by deforming the action with a fermion bilinear term. The results for the original system are obtained by extrapolations with respect to the deformation parameter. We demonstrate the power of this approach by applying it to a simple matrix model, in which spontaneous symmetry breaking from SO(4) to SO(2) is expected to occur due to the phase of the complex fermion determinant. Unlike previous work based on a reweighting-type method, we are able to determine the true vacuum by calculating the order parameters, which agree with the prediction by the Gaussian expansion method.

On the axial anomalies in external tensor fields

International Nuclear Information System (INIS)

Khudaverdyan, O.M.; Mkrtchyan, R.L.; Zurabyan, L.A.

1985-01-01

Computation of the axial anomaly for Dirac fermions in external tensor fields is studied. The sequence of the supersymmetric one-dimensional models is presented. Their supercharges are equal, after quantization, to Dirac operators in external tensor fields, and the density of Witten's partition function gives the anomaly. It is shown that action in the corresponding path integral differs from the classical one. Gaussian approximation gives the anomaly only in the case of third-rank tensor with zero exterior derivative and in that case anomaly is calculated in all dimensions. The interpretation of that field as the torsion of gravitational field and also connection with the results of Witten and Alvarez-Gaume and Atiyah-Singer index theorem are discussed

AdS5 black holes with fermionic hair

International Nuclear Information System (INIS)

Burrington, Benjamin A.; Liu, James T.; Sabra, W. A.

2005-01-01

The study of new Bogomol'nyi-Prasad-Sommerfield (BPS) objects in AdS 5 has led to a deeper understanding of AdS/CFT. To help complete this picture, and to fully explore the consequences of the supersymmetry algebra, it is also important to obtain new solutions with bulk fermions turned on. In this paper we construct superpartners of the 1/2 BPS black hole in AdS 5 using a natural set of fermion zero modes. We demonstrate that these superpartners, carrying fermionic hair, have conserved charges differing from the original bosonic counterpart. To do so, we find the R-charge and dipole moment of the new system, as well as the mass and angular momentum, defined through the boundary stress tensor. The complete set of superpartners fits nicely into a chiral representation of AdS 5 supersymmetry, and the spinning solutions have the expected gyromagnetic ratio, g=1

On the energy-momentum tensor in Moyal space

International Nuclear Information System (INIS)

Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois

2015-01-01

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)

Lorentz invariance and the zero-point stress-energy tensor

OpenAIRE

Visser, Matt

2016-01-01

Some 65 years ago (1951) Wolfgang Pauli noted that the net zero-point energy density could be set to zero by a carefully fine-tuned cancellation between bosons and fermions. In the current article I will argue in a slightly different direction: The zero-point energy density is only one component of the zero-point stress energy tensor, and it is this tensor quantity that is in many ways the more fundamental object of interest. I shall demonstrate that Lorentz invariance of the zero-point stres...

Nonlinear system modeling based on bilinear Laguerre orthonormal bases.

Science.gov (United States)

Garna, Tarek; Bouzrara, Kais; Ragot, José; Messaoud, Hassani

2013-05-01

This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, such reduction still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al.. The bilinear-Laguerre model as well as the proposed pole optimization algorithm are illustrated and tested on a numerical simulations and validated on the Continuous Stirred Tank Reactor (CSTR) System. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Reduction schemes for one-loop tensor integrals

International Nuclear Information System (INIS)

Denner, A.; Dittmaier, S.

2006-01-01

We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex

On classical state space realizability of bilinear inout-output differential equations

OpenAIRE

Kotta, U.; Mullari, T.; Kotta, P.; Zinober, A.S.I.

2006-01-01

This paper studies the realizability property of continuous-time bilinear i/o equations in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The paper proves that the 2nd order bilinear i/o differential equation, unlike the discrete-time case, is always realizable in the classical state space form. The complete list of 3rd and 4th order realizable i/o bilinear models is given and two subclasses of realizable i...

Bosonization of free Weyl fermions

Science.gov (United States)

Marino, E. C.

2017-03-01

We generalize the method of bosonization, in its complete form, to a spacetime with 3  +  1 dimensions, and apply it to free Weyl fermion fields, which thereby, can be expressed in terms of a boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The result may have interesting consequences both in condensed matter and in particle physics. In the former, the bosonized form of the Weyl chiral currents provides a simple explanation for the angle-dependent magneto-conductance recently observed in materials known as Weyl semimetals. In the latter, conversely, since electrons can be thought of as a combination of left and right Weyl fermions, our result suggests the possibility of a unified description of the elementary particles, which undergo the fundamental interactions, with the mediators of such interactions, namely, the gauge fields. This would fulfill the pioneering attempt of Skyrme, to unify the particles with their interaction mediators (Skyrme 1962 Nucl. Phys. 31 556).

Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion

Science.gov (United States)

Shimizu, Yuya; Kuramashi, Yoshinobu

2018-02-01

We have made a detailed study of the phase structure for the lattice Schwinger model with one flavor of Wilson fermion on the (m ,g ) plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole (m ,g )=(-2 ,0 ), while the parity-breaking transition line ends at the physical pole (m ,g )=(0 ,0 ). In addition, our analysis of scaling dimensions indicates that a conformal field theory with SU(2) symmetry arises on the line of m =-2 .

Towards critical physics in 2+1d with U(2N)-invariant fermions

Energy Technology Data Exchange (ETDEWEB)

Hands, Simon [Department of Physics, College of Science, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom)

2016-11-04

Interacting theories of N relativistic fermion flavors in reducible spinor representations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall separation L{sub s} is made large. The Gross-Neveu (GN) model is studied in the large-N limit and an exponential acceleration of convergence to the large-L{sub s} limit is demonstrated if the usual parity-invariant mass mψ̄ψ is replaced by the U(2N)-equivalent im{sub 3}ψ̄γ{sub 3}ψ. The GN model and two lattice variants of the Thirring model are simulated for N=2 using a hybrid Monte Carlo algorithm, and studies made of the symmetry-breaking bilinear condensate and its associated susceptibility, the axial Ward identity, and the mass spectrum of both fermion and meson excitations. Comparisons are made with existing results obtained using staggered fermions. For the GN model a symmetry-breaking phase transition is observed, the Ward identity is recovered, and the spectrum found to be consistent with large-N expectations. There appears to be no obstruction to the study of critical UV fixed-point physics using DWF. For the Thirring model the Ward identity is not recovered, the spectroscopy measurements are inconclusive, and no symmetry breaking is observed all the way up to the effective strong coupling limit. This is consistent with a critical Thirring flavor number N{sub c}<2, contradicting earlier staggered fermion results.

Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series

Directory of Open Access Journals (Sweden)

Sabarinsyah

2017-06-01

Full Text Available In this study a generalization of the Riesz representation theorem on non-degenerate bilinear spaces, particularly on spaces of truncated Laurent series, was developed. It was shown that any linear functional on a non-degenerate bilinear space is representable by a unique element of the space if and only if its kernel is closed. Moreover an explicit equivalent condition can be identified for the closedness property of the kernel when the bilinear space is a space of truncated Laurent series.

Stabilization of third-order bilinear systems using constant controls

Directory of Open Access Journals (Sweden)

A. E. Golubev

2014-01-01

Full Text Available This paper deals with the zero equilibrium stabilization for dynamical systems that have control input singularities. A dynamical system with scalar control input is called nonregular if the coefficient of input becomes null on a subset of the phase space that contains the origin. One of the classes of nonregular dynamical systems is represented by bilinear systems. In case of second-order bilinear systems the necessary and sufficient conditions for the zero equilibrium stabilizability are known in the literature. However, in general case the stabilization problem in the presence of control input singularities has not been solved yet.In this note we solve the problem of the zero equilibrium stabilization for the third-order bilinear dynamical systems given in a canonical form. The solution is found in the class of constant controls. The necessary and sufficient conditions are obtained for the zero equilibrium stabilizability of the bilinear systems in question.The dependence of the zero equilibrium stabilizability on system parameter values is analyzed. The general criteria of stabilizability by means of constant controls are given for the bilinear systems in question. In case when all the system parameters have nonzero values the necessary and sufficient stabilizability conditions are proved. The case when some of the parameters are equal to zero is also considered.Further research can be focused on extending the obtained results to a higher-order case of bilinear and affine dynamical systems. The solution of the considered stabilization problem should also be found not only within constant controls but also in a class of state feedbacks, particularly, in the case when stabilizing constant control does not exist.One of the potential application areas for the obtained theoretical results is automatic control of technical plants like unmanned aerial vehicles and mobile robots.

Vector bilinear autoregressive time series model and its superiority ...

African Journals Online (AJOL)

In this research, a vector bilinear autoregressive time series model was proposed and used to model three revenue series (X1, X2, X3) . The “orders” of the three series were identified on the basis of the distribution of autocorrelation and partial autocorrelation functions and were used to construct the vector bilinear models.

Theoretical study of the relativistic molecular rotational g-tensor

International Nuclear Information System (INIS)

Aucar, I. Agustín; Gomez, Sergio S.; Giribet, Claudia G.; Ruiz de Azúa, Martín C.

2014-01-01

An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH + (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH + systems. Only for the sixth-row Rn atom a significant deviation of this relation is found

Theoretical study of the relativistic molecular rotational g-tensor

Energy Technology Data Exchange (ETDEWEB)

Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)

2014-11-21

An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.

Bilinear models for inter- and intra-patient variation of the prostate

International Nuclear Information System (INIS)

Jeong, Y; Radke, R J; Lovelock, D M

2010-01-01

We propose bilinear models for capturing and effectively decoupling the expected shape variations of an organ both across the patient population and within a specific patient. Bilinear models have been successfully introduced in other areas of computer vision, but they have rarely been used in medical imaging applications. Our particular interest is in modeling the shape variation of the prostate for potential use in radiation therapy treatment planning. Using a dataset of 204 prostate shapes contoured from CT imagery of 12 different patients, we build bilinear models and show that they can fit both training and testing shapes accurately. We also show how the bilinear model can adapt to a new patient using only a few example shapes, producing a patient-specific model that also reflects expected content variation learnt from a broader population. Finally, we evaluate the training and testing projection error, adaptation performance and image segmentation accuracy of the bilinear model compared to linear principal component analysis and hierarchical point distribution models with the same number of parameters.

An implementation for the algorithm of the Hirota bilinear Baecklund transformation of integrable hierarchies

International Nuclear Information System (INIS)

Yu Guofu; Duan Qihua

2010-01-01

In this paper, based on the Hirota bilinear method, a reliable algorithm for generating the bilinear Baecklund transformation (BT) of integrable hierarchies is described. With the help of Maple symbolic computation the algorithm would be very helpful and powerful for looking for the bilinear BT of integrable systems especially for those high-order integrable hierarchies. The BTs of bilinear Ramani hierarchy are deduced for the first time by using the algorithm.

A supersymmetric SYK-like tensor model

Energy Technology Data Exchange (ETDEWEB)

Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence, RI, 02912 (United States)

2017-05-11

We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

A supersymmetric SYK-like tensor model

International Nuclear Information System (INIS)

Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia

2017-01-01

We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.

Hamiltonian quantization of self-dual tensor fields and a bosonic Nielsen-Ninomiya theorem

International Nuclear Information System (INIS)

Tang Waikeung

1989-01-01

The quantization of self-dual tensor fields is carried out following the procedure of Batalin and Fradkin. The (anti) self-duality constraints (either fermionic or bosonic) in the action leads to the gravitational anomaly. In the process of gauge fixing, the impossibility of the co-existence of a positive hamiltonian and covariant action is shown. A version of the Nielsen-Ninomiya theorem applies to self-dual tensor fields viz. the lattice version of the theory shows species doubling with zero net chirality. (orig.)

Fermions in noncommutative emergent gravity

International Nuclear Information System (INIS)

Klammer, D.

2010-01-01

Noncommutative emergent gravity is a novel framework disclosing how gravity is contained naturally in noncommutative gauge theory formulated as a matrix model. It describes a dynamical space-time which itself is a four-dimensional brane embedded in a higher-dimensional space. In noncommutative emergent gravity, the metric is not a fundamental object of the model; rather it is determined by the Poisson structure and by the induced metric of the embedding. In this work the coupling of fermions to these matrix models is studied from the point of view of noncommutative emergent gravity. The matrix Dirac operator as given by the IKKT matrix model defines an appropriate coupling for fermions to an effective gravitational metric of noncommutative four-dimensional spaces that are embedded into a ten-dimensional ambient space. As it turns out this coupling is non-standard due to a spin connection that vanishes in the preferred but unobservable coordinates defined by the model. The purpose of this work is to study the one-loop effective action of this approach. Standard results of the literature cannot be applied due to this special coupling of the fermions. However, integrating out these fields in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the noncommutative structure to the Riemann tensor, and a dilaton-like term. It remains to be understood what the effects of these terms are and whether they can be avoided. In a second step, the existence of a duality between noncommutative gauge theory and gravity which explains the phenomenon of UV/IR mixing as a gravitational effect is discussed. We show how the gravitational coupling of fermions can be interpreted as a coupling of fermions to gauge fields, which suffers then from UV/IR mixing. This explanation does not render the model finite but it reveals why some UV/IR mixing remains even in supersymmetric models, except in the N

An Interaction Measure for Control Configuration Selection for Multivariable Bilinear Systems

DEFF Research Database (Denmark)

Shaker, Hamid Reza; Stoustrup, Jakob

2013-01-01

are needed to be controlled, are nonlinear and linear models are insufficient to describe the behavior of the processes. The focus of this paper is on the problem of control configuration selection for a class of nonlinear systems which is known as bilinear systems. A gramian-based interaction measure...... for control configuration selection of MIMO bilinear processes is described. In general, most of the results on the control configuration selection, which have been proposed so far, can only support linear systems. The proposed gramian-based interaction measure not only supports bilinear processes but also...

A numerical algorithm for modelling boson-fermion stars in dilatonic gravity

CERN Document Server

Boyadzhiev, T L; Todorov, M D; Yazadjiev, S S

2002-01-01

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) R sub s , and the second one represents the frequency OMEGA of the time oscillations of the boson field. To solve this problem, the whole space [0, infinity) is splitted into two domains: internal [0, R sub s] (inside the star) and external [R sub s , infinity) (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 ma...

Short-ranged radial and tensor correlations in nuclear many-body systems

International Nuclear Information System (INIS)

Neff, T.; Feldmeier, H.

2003-01-01

The unitary correlation operator method (UCOM) is applied to realistic potentials. The effects of tensor correlations are investigated. The resulting phase shift equivalent correlated interactions are used in the no-core shell model for light nuclei and for mean-field calculations in the Fermionic Molecular Dynamics model for nuclei up to mass A=48. (orig.)

Properties of the stress tensor in more than two dimensions

International Nuclear Information System (INIS)

Cappelli, A.

1988-03-01

Some aspects of conformal invariance in more than two dimensions are analysed. In this case conformal (Weyl) transformations of the metric are not realized in general by coordinate transformations. The operator product expansion of the stress tensor is investigated by means of examples in the free bosonic and fermionic theories. The effective action for the general form of the trace anomaly is built in four dimensions and the Wess-Zumino consistency conditions are discussed. This gives the anomalous transformation law of the stress tensor and the relation to the Casimir effect in the geometry R x S 3 . The explicit computation of the bosonic partition function provides a check

Smooth surfaces from rational bilinear patches

KAUST Repository

Shi, Ling; Wang, Jun; Pottmann, Helmut

2014-01-01

Smooth freeform skins from simple panels constitute a challenging topic arising in contemporary architecture. We contribute to this problem area by showing how to approximate a negatively curved surface by smoothly joined rational bilinear patches

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

Science.gov (United States)

Lubicz, Vittorio; Riggio, Lorenzo; Salerno, Giorgio; Simula, Silvano; Tarantino, Cecilia

2018-03-01

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

Time Optimal Control Laws for Bilinear Systems

Directory of Open Access Journals (Sweden)

Salim Bichiou

2018-01-01

Full Text Available The aim of this paper is to determine the feedforward and state feedback suboptimal time control for a subset of bilinear systems, namely, the control sequence and reaching time. This paper proposes a method that uses Block pulse functions as an orthogonal base. The bilinear system is projected along that base. The mathematical integration is transformed into a product of matrices. An algebraic system of equations is obtained. This system together with specified constraints is treated as an optimization problem. The parameters to determine are the final time, the control sequence, and the states trajectories. The obtained results via the newly proposed method are compared to known analytical solutions.

The bilinear complexity and practical algorithms for matrix multiplication

Science.gov (United States)

Smirnov, A. V.

2013-12-01

A method for deriving bilinear algorithms for matrix multiplication is proposed. New estimates for the bilinear complexity of a number of problems of the exact and approximate multiplication of rectangular matrices are obtained. In particular, the estimate for the boundary rank of multiplying 3 × 3 matrices is improved and a practical algorithm for the exact multiplication of square n × n matrices is proposed. The asymptotic arithmetic complexity of this algorithm is O( n 2.7743).

Euclidean supersymmetric solutions with the self-dual Weyl tensor

Directory of Open Access Journals (Sweden)

Masato Nozawa

2017-07-01

Full Text Available We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N=2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski–Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski–Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski–Tod form. This formalism enables us to show that the self-dual Reissner–Nordström–Taub–NUT–AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski–Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing–Yano tensor.

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.

The Calogero model - anyonic representation, fermionic extension and supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Brink, L [Inst. of Theoretical Physics, Goeteborg (Sweden); Hansson, T H [Inst. of Theoretical Physics, Univ. of Stockholm (Sweden); Konstein, S [Dept. of Theoretical Physics, P.N. Lebedev Inst., Moscow (Russian Federation); Vasiliev, M A [Dept. of Theoretical Physics, P.N. Lebedev Inst., Moscow (Russian Federation)

1993-07-26

We discuss several applications and extensions of our previous operator solution of the N-body quantum-mechanical Calogero problem, i.e. N particles in one dimension subject to a two-body interaction of the form 1/2[Sigma][sub i,j] (x[sub i]-x[sub j])[sup 2]+g/(x[sub i]-x[sub j])[sup 2]. Using a complex representation of the deformed Heisenberg algebra underlying the Calogero model, we explicitly establish the equivalence between this system and anyons in the lowest Landau level. A construction based on supersymmetry is used to extend our operator method to include fermions, and we obtain an explicit solution of the supersymmetric Calogero model constructed by Freedman and Mende. We also show how the dynamical OSp(2; 2) supersymmetry is realized by bilinears of modified creation and annihilation operators, and how to construct a supersymmetric extension of the deformed Heisenberg algebra. (orig.)

TensorLy: Tensor Learning in Python

OpenAIRE

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...

Wilson Fermions with Four Fermion Interactions

DEFF Research Database (Denmark)

Rantaharju, Jarno; Drach, Vincent; Hietanen, Ari

2015-01-01

We present a lattice study of a four fermion theory, known as Nambu Jona-Lasinio (NJL) theory, via Wilson fermions. Four fermion interactions naturally occur in several extensions of the Standard Model as a low energy parameterisation of a more fundamental theory. In models of dynamical electroweak...

Fermion production despite fermion number conservation

International Nuclear Information System (INIS)

Bock, W.; Hetrick, J.E.; Smit, J.

1995-01-01

Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. Both the sharp momentum cutoff and the lattice regulator break gauge invariance. In the case of the lattice model a mass counterterm for the gauge field is sufficient to restore gauge invariance in the perturbative regime. A study of the vacuum energy shows however that the perturbative counterterm is insufficient in a nonperturbative setting and that further quartic counterterms are needed. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories. ((orig.))

Free massless fermionic fields of arbitrary spin in d-dimensional anti-de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A

1988-04-25

Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d-2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.

Identifiability analysis of rotational diffusion tensor and electronic transition moments measured in time-resolved fluorescence depolarization experiment

International Nuclear Information System (INIS)

Szubiakowski, Jacek P.

2014-01-01

The subject of this paper is studies of the deterministic identifiability of molecular parameters, such as rotational diffusion tensor components and orientation of electronic transition moments, resulting from the time-resolved fluorescence anisotropy experiment. In the most general case considered, a pair of perpendicularly polarized emissions enables the unique determination of all the rotational diffusion tensor's principal components. The influence of the tensor's symmetry and the associated degeneration of its eigenvalues on the identifiability of the electronic transitions moments is systematically investigated. The analysis reveals that independently of the rotational diffusion tensor's symmetry, the transition moments involved in photoselection and emission processes cannot be uniquely identified without a priori information about their mutual orientation or their orientation with respect to the principal axes of the tensor. Moreover, it is shown that increasing the symmetry of the rotational diffusion tensor deteriorates the degree of the transition moments identifiability. To obtain these results analytically, a novel approach to solve bilinear system of equations for Markov parameters is applied. The effect of the additional information, obtained from fluorescence measurements for different molecular mobilities, to improve the identifiability at various levels of analysis is shown. The effectiveness and reliability of the target analysis method for experimental determination of the molecular parameters is also discussed

Exploring the structure of the quenched QCD vacuum with overlap fermions

International Nuclear Information System (INIS)

Ilgenfritz, E.M.; Koller, K.; Koma, Y.; Schierholz, G.; Deutsches Elektronen-Synchrotron; Streuer, T.; Weinberg, V.; Freie Univ. Berlin

2007-05-01

Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure. (orig.)

Some integrable maps and their Hirota bilinear forms

Science.gov (United States)

Hone, A. N. W.; Kouloukas, T. E.; Quispel, G. R. W.

2018-01-01

We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the Laurent property, and the tropical (or ultradiscrete) analogue of this homogeneous recurrence confirms the quadratic degree growth found empirically by Demskoi et al. We prove that the tau function also satisfies two different bilinear equations, each of which is a reduction of the Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence). Furthermore, these bilinear equations are related to reductions of particular two-dimensional integrable lattice equations, of discrete KdV or discrete Toda type. These connections, as well as the cluster algebra structure of the bilinear equations, allow a direct construction of Poisson brackets, Lax pairs and first integrals for the birational maps. As a consequence of the latter results, we show how each member of the family can be lifted to a system that is integrable in the Liouville sense, clarifying observations made previously in the original DTKQ case.

Direct approach to operator conformal constructions: from fermions to primary fields

International Nuclear Information System (INIS)

Halpern, M.B.

1989-01-01

I discuss the direct solution of Sugawara and coset constructions, including a path to construction of the primary fields. The basic tools are (1) a construction of affine-conformal highest-weight states, pretensors and tensors form quantum-irreducible representations of the currents of affine g, and (2) construction of primary fields by factorization and boosting of the pretensors. Large classes of pretensors are easily obtained in fermionic constructions, and guesswork is minimized with factorization of bosonized fermionic pretensors: The simplest case constructs conformal-weights h g =mN(n--N)/2n of SU m (n) and h K =mN(n--N)/n of SU m (n)direct-product SU m (n)/SU 2m (n) and extension to simply-laced g is clear. More general cases are left for future study. copyright Academic Prss, Inc. 1989

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

Science.gov (United States)

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Gambhir, Arjun S.; Orginos, Kostas; Savage, Martin J.; Shanahan, Phiala E.; Wagman, Michael L.; Winter, Frank; Nplqcd Collaboration

2018-04-01

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass mπ˜806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O (10 %), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

Nonperturbative Renormalization of Composite Operators with Overlap Fermions

Energy Technology Data Exchange (ETDEWEB)

J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams

2005-12-01

We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

Bilinear common spatial pattern for single-trial ERP-based rapid serial visual presentation triage

Science.gov (United States)

Yu, K.; Shen, K.; Shao, S.; Ng, W. C.; Li, X.

2012-08-01

Common spatial pattern (CSP) analysis is a useful tool for the feature extraction of event-related potentials (ERP). However, CSP is essentially time invariant, and thus unable to exploit the temporal information of ERP. This paper proposes a variant of CSP, namely bilinear common spatial pattern (BCSP), which is capable of accommodating both spatial and temporal information. BCSP generalizes CSP through iteratively optimizing bilinear filters. These bilinear filters constitute a spatio-temporal subspace in which the separation between two conditions is maximized. The method is unique in the sense that it is mathematically intuitive and simple, as all the bilinear filters are obtained by maximizing the power ratio as CSP does. The proposed method was evaluated on 20 subjects’ ERP data collected in rapid serial visual presentation triage experiments. The results show that BCSP achieved significantly higher average test accuracy (12.3% higher, p < 0.001).

Bilinear phase-plane distribution functions and positivity

NARCIS (Netherlands)

Janssen, A.J.E.M.

1985-01-01

There is a theorem of Wigner that states that phase-plane distribution functions involving the state bilinearly and having correct marginals must take negative values for certain states. The purpose of this paper is to support the statement that these phase-plane distribution functions are for

Universal formula for the energy–momentum tensor via a flow equation in the Gross–Neveu model

International Nuclear Information System (INIS)

Suzuki, Hiroshi

2015-01-01

For the fermion field in the two-dimensional Gross–Neveu model, we introduce a flow equation that allows a simple 1/N expansion. By employing the 1/N expansion, we examine the validity of a universal formula for the energy–momentum tensor which is based on the small flow-time expansion. We confirm that the formula reproduces a correct normalization and the conservation law of the energy–momentum tensor by computing the translation Ward–Takahashi relation in the leading non-trivial order in the 1/N expansion. Also, we confirm that the expectation value at finite temperature correctly reproduces thermodynamic quantities. These observations support the validity of a similar construction of the energy–momentum tensor via the gradient/Wilson flow in lattice gauge theory

Diffusion-accelerated solution of the 2-D x-y Sn equations with linear-bilinear nodal differencing

International Nuclear Information System (INIS)

Wareing, T.A.; Walters, W.F.; Morel, J.E.

1994-01-01

Recently a new diffusion-synthetic acceleration scheme was developed for solving the 2-D S n Equations in x-y geometry with bilinear-discontinuous finite element spatial discretization using a bilinear-discontinuous diffusion differencing scheme for the diffusion acceleration equations. This method differs from previous methods in that it is conditional efficient for problems with isotropic or nearly isotropic scattering. We have used the same bilinear-discontinuous diffusion scheme, and associated solution technique, to accelerate the x-y geometry S n equations with linear-bilinear nodal spatial differencing. We find that this leads to an unconditionally efficient solution method for problems with isotropic or nearly isotropic scattering. computational results are given which demonstrate this property

Signature scheme based on bilinear pairs

Science.gov (United States)

Tong, Rui Y.; Geng, Yong J.

2013-03-01

An identity-based signature scheme is proposed by using bilinear pairs technology. The scheme uses user's identity information as public key such as email address, IP address, telephone number so that it erases the cost of forming and managing public key infrastructure and avoids the problem of user private generating center generating forgery signature by using CL-PKC framework to generate user's private key.

Adaptive fuzzy bilinear observer based synchronization design for generalized Lorenz system

International Nuclear Information System (INIS)

Baek, Jaeho; Lee, Heejin; Kim, Seungwoo; Park, Mignon

2009-01-01

This Letter proposes an adaptive fuzzy bilinear observer (FBO) based synchronization design for generalized Lorenz system (GLS). The GLS can be described to TS fuzzy bilinear generalized Lorenz model (FBGLM) with their states immeasurable and their parameters unknown. We design an adaptive FBO based on TS FBGLM for synchronization. Lyapunov theory is employed to guarantee the stability of error dynamic system via linear matrix equalities (LMIs) and to derive the adaptive laws to estimate unknown parameters. Numerical example is given to demonstrate the validity of our proposed adaptive FBO approach for synchronization.

Plethystic vertex operators and boson-fermion correspondences

International Nuclear Information System (INIS)

Fauser, Bertfried; Jarvis, Peter D; King, Ronald C

2016-01-01

We study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), 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 π . Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π , 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. (paper)

Plethystic vertex operators and boson-fermion correspondences

Science.gov (United States)

Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C.

2016-10-01

We study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), 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 π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, 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.

The Bilinear Product Model of Hysteresis Phenomena

Science.gov (United States)

Kádár, György

1989-01-01

In ferromagnetic materials non-reversible magnetization processes are represented by rather complex hysteresis curves. The phenomenological description of such curves needs the use of multi-valued, yet unambiguous, deterministic functions. The history dependent calculation of consecutive Everett-integrals of the two-variable Preisach-function can account for the main features of hysteresis curves in uniaxial magnetic materials. The traditional Preisach model has recently been modified on the basis of population dynamics considerations, removing the non-real congruency property of the model. The Preisach-function was proposed to be a product of two factors of distinct physical significance: a magnetization dependent function taking into account the overall magnetization state of the body and a bilinear form of a single variable, magnetic field dependent, switching probability function. The most important statement of the bilinear product model is, that the switching process of individual particles is to be separated from the book-keeping procedure of their states. This empirical model of hysteresis can easily be extended to other irreversible physical processes, such as first order phase transitions.

Lyapunov equation for infinite-dimensional discrete bilinear systems

International Nuclear Information System (INIS)

Costa, O.L.V.; Kubrusly, C.S.

1991-03-01

Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)

Smooth surfaces from bilinear patches: Discrete affine minimal surfaces

KAUST Repository

Kä ferbö ck, Florian; Pottmann, Helmut

2013-01-01

Motivated by applications in freeform architecture, we study surfaces which are composed of smoothly joined bilinear patches. These surfaces turn out to be discrete versions of negatively curved affine minimal surfaces and share many properties

Highly imbalanced fermion-fermion mixtures in one dimension

International Nuclear Information System (INIS)

Recher, Christian

2013-01-01

In the framework of exactly solvable quantum many-body systems we study models of interacting spin one-half Fermions in one dimension. The first part deals with systems of spin one-half Fermions which interact via repulsive contact interaction. A reformulation of the Bethe-Ansatz solvable many-body wave function is presented. This simplifies considerably the calculations for the highly imbalanced case, where very few particles of one species (minority Fermions) are present. For the other particle species (majority Fermions) the thermodynamic limit is taken. We assume the majority Fermions to be in the ground state such that their non-interacting momentum distribution is a Fermi-sea. Upon this we consider excitations where the particles of the minority species may occupy an arbitrary state within the Fermi-sea. In the case of only a single minority Fermion, the many-body wave function can be expressed as a determinant. This allows us to derive exact thermodynamic expressions for several expectation values as well as for the density-density correlation function. Moreover it is possible to find closed expressions for the single particle Green's function. All of the above mentioned quantities show a non-trivial dependence on the minority particle's momentum. In particular the Green's function in the Tonks-Girardeau regime of hardcore interaction is shown to undergo a transition from the one of impenetrable Bosons to that of free Fermions as the extra particle's momentum varies from the core to the edge of the Fermi-sea. This transition becomes manifest in an algebraic asymptotic decay of the Green's function. If two minority Fermions are present, the many-body wave function turns out to be more complicated. Nevertheless it is possible to derive exact expressions for the two and the three particle density-density correlation functions. Furthermore we calculate the system's total energy and based on that, identify terms which have a natural

Majorana fermion codes

International Nuclear Information System (INIS)

Bravyi, Sergey; Terhal, Barbara M; Leemhuis, Bernhard

2010-01-01

We initiate the study of Majorana fermion codes (MFCs). These codes can be viewed as extensions of Kitaev's one-dimensional (1D) model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of MFCs is to protect quantum information against low-weight fermionic errors, that is, operators acting on sufficiently small subsets of fermionic modes. We examine to what extent MFCs can surpass qubit stabilizer codes in terms of their stability properties. A general construction of 2D MFCs is proposed that combines topological protection based on a macroscopic code distance with protection based on fermionic parity conservation. Finally, we use MFCs to show how to transform any qubit stabilizer code to a weakly self-dual CSS code.

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

International Nuclear Information System (INIS)

Reshetnyak, A.

2013-01-01

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

Note on Integer-Valued Bilinear Time Series Models

NARCIS (Netherlands)

Drost, F.C.; van den Akker, R.; Werker, B.J.M.

2007-01-01

Summary. This note reconsiders the nonnegative integer-valued bilinear processes introduced by Doukhan, Latour, and Oraichi (2006). Using a hidden Markov argument, we extend their result of the existence of a stationary solution for the INBL(1,0,1,1) process to the class of superdiagonal INBL(p; q;

Tensor constructions of open string theories. I. Foundations

International Nuclear Information System (INIS)

Gaberdiel, M.R.; Zwiebach, B.

1997-01-01

The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A ∞ algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are off-shell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense. It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a space-time interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group. (orig.)

Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors

KAUST Repository

Elmetennani, Shahrazed

2016-11-09

This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature to track a set reference despite the unpredictable varying working conditions. In this brief, a bilinear model-based robust Lyapunov control is proposed to achieve the control objectives with robustness to the environmental changes. The bilinear model is a reduced order approximate representation of the solar collector, which is derived from the hyperbolic distributed equation describing the heat transport dynamics by means of a dynamical Gaussian interpolation. Using the bilinear approximate model, a robust control strategy is designed applying Lyapunov stability theory combined with a phenomenological representation of the system in order to stabilize the tracking error. On the basis of the error analysis, simulation results show good performance of the proposed controller, in terms of tracking accuracy and convergence time, with limited measurement even under unfavorable working conditions. Furthermore, the presented work is of interest for a large category of dynamical systems knowing that the solar collector is representative of physical systems involving transport phenomena constrained by unknown external disturbances.

Noninteractive Verifiable Outsourcing Algorithm for Bilinear Pairing with Improved Checkability

Directory of Open Access Journals (Sweden)

Yanli Ren

2017-01-01

Full Text Available It is well known that the computation of bilinear pairing is the most expensive operation in pairing-based cryptography. In this paper, we propose a noninteractive verifiable outsourcing algorithm of bilinear pairing based on two servers in the one-malicious model. The outsourcer need not execute any expensive operation, such as scalar multiplication and modular exponentiation. Moreover, the outsourcer could detect any failure with a probability close to 1 if one of the servers misbehaves. Therefore, the proposed algorithm improves checkability and decreases communication cost compared with the previous ones. Finally, we utilize the proposed algorithm as a subroutine to achieve an anonymous identity-based encryption (AIBE scheme with outsourced decryption and an identity-based signature (IBS scheme with outsourced verification.

Local bilinear multiple-output quantile/depth regression

Czech Academy of Sciences Publication Activity Database

Hallin, M.; Lu, Z.; Paindaveine, D.; Šiman, Miroslav

2015-01-01

Roč. 21, č. 3 (2015), s. 1435-1466 ISSN 1350-7265 R&D Projects: GA MŠk(CZ) 1M06047 Institutional support: RVO:67985556 Keywords : conditional depth * growth chart * halfspace depth * local bilinear regression * multivariate quantile * quantile regression * regression depth Subject RIV: BA - General Mathematics Impact factor: 1.372, year: 2015 http://library.utia.cas.cz/separaty/2015/SI/siman-0446857.pdf

Damage Detection Based on Cross-Term Extraction from Bilinear Time-Frequency Distributions

Directory of Open Access Journals (Sweden)

Ma Yuchao

2014-01-01

Full Text Available Abundant damage information is implicated in the bilinear time-frequency distribution of structural dynamic signals, which could provide effective support for structural damage identification. Signal time-frequency analysis methods are reviewed, and the characters of linear time-frequency distribution and bilinear time-frequency distribution typically represented by the Wigner-Ville distribution are compared. The existence of the cross-term and its application in structural damage detection are demonstrated. A method of extracting the dominant term is proposed, which combines the short-time Fourier spectrum and Wigner-Ville distribution; then two-dimensional time-frequency transformation matrix is constructed and the complete cross-term is extracted finally. The distribution character of which could be applied to the structural damage identification. Through theoretical analysis, model experiment and numerical simulation of the girder structure, the change rate of cross-term amplitude is validated to identify the damage location and degree. The effectiveness of the cross-term of bilinear time-frequency distribution for damage detection is confirmed and the analytical method of damage identification used in structural engineering is available.

Fractional fermions

International Nuclear Information System (INIS)

Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1984-01-01

The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)

Frequency Interval Cross Gramians for Linear and Bilinear Systems

DEFF Research Database (Denmark)

Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza

2017-01-01

In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the freque...

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

International Nuclear Information System (INIS)

Wang, Lei; Corboz, Philippe; Troyer, Matthias

2014-01-01

Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point V/t=1.356(1) with the critical exponents ν=0.80(3) and η=0.302(7). Compatible results for the transition point are also obtained with infinite projected entangled-pair states. (paper)

Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics

OpenAIRE

Leibov Roman

2017-01-01

This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems ...

Non-perturbative renormalization in coordinate space for Nf=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action

International Nuclear Information System (INIS)

Cichy, Krzysztof; Adam Mickiewicz Univ., Poznan; Jansen, Karl; Korcyl, Piotr; Jagiellonian Univ., Krakow

2012-07-01

We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N f =2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)

Simulating lattice fermions by microcanonically averaging out the nonlocal dependence of the fermionic action

International Nuclear Information System (INIS)

Azcoiti, V.; Cruz, A.; Di Carlo, G.; Grillo, A.F.; Vladikas, A.

1991-01-01

We attempt to increase the efficiency of simulations of dynamical fermions on the lattice by calculating the fermionic determinant just once for all the values of the theory's gauge coupling and flavor number. Our proposal is based on the determination of an effective fermionic action by the calculation of the fermionic determinant averaged over configurations at fixed gauge energy. The feasibility of our method is justified by the observed volume dependence of the fluctuations of the logarithm of the determinant. The algorithm we have used in order to calculate the fermionic determinant, based on the determination of all the eigenvalues of the fermionic matrix at zero mass, also enables us to obtain results at any fermion mass, with a single fermionic simulation. We test the method by simulating compact lattice QED, finding good agreement with other standard calculations. New results on the phase transition of compact QED with massless fermions on 6 4 and 8 4 lattices are also presented

Fermionic One-Way Quantum Computation

International Nuclear Information System (INIS)

Cao Xin; Shang Yun

2014-01-01

Fermions, as another major class of quantum particles, could be taken as carriers for quantum information processing beyond spins or bosons. In this work, we consider the fermionic generalization of the one-way quantum computation model and find that one-way quantum computation can also be simulated with fermions. In detail, using the n → 2n encoding scheme from a spin system to a fermion system, we introduce the fermionic cluster state, then the universal computing power with a fermionic cluster state is demonstrated explicitly. Furthermore, we show that the fermionic cluster state can be created only by measurements on at most four modes with |+〉 f (fermionic Bell state) being free

Fermionic cosmologies

International Nuclear Information System (INIS)

Chimento, L P; Forte, M; Devecchi, F P; Kremer, G M; Ribas, M O; Samojeden, L L

2011-01-01

In this work we review if fermionic sources could be responsible for accelerated periods during the evolution of a FRW universe. In a first attempt, besides the fermionic source, a matter constituent would answer for the decelerated periods. The coupled differential equations that emerge from the field equations are integrated numerically. The self-interaction potential of the fermionic field is considered as a function of the scalar and pseudo-scalar invariants. It is shown that the fermionic field could behave like an inflaton field in the early universe, giving place to a transition to a matter dominated (decelerated) period. In a second formulation we turn our attention to analytical results, specifically using the idea of form-invariance transformations. These transformations can be used for obtaining accelerated cosmologies starting with conventional cosmological models. Here we reconsider the scalar field case and extend the discussion to fermionic fields. Finally we investigate the role of a Dirac field in a Brans-Dicke (BD) context. The results show that this source, in combination with the BD scalar, promote a final eternal accelerated era, after a matter dominated period.

Emergent gravity from vanishing energy-momentum tensor

Energy Technology Data Exchange (ETDEWEB)

Carone, Christopher D.; Erlich, Joshua [High Energy Theory Group, Department of Physics, College of William and Mary,Williamsburg, VA 23187-8795 (United States); Vaman, Diana [Department of Physics, University of Virginia,Box 400714, Charlottesville, VA 22904 (United States)

2017-03-27

A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.

Emergent gravity from vanishing energy-momentum tensor

International Nuclear Information System (INIS)

Carone, Christopher D.; Erlich, Joshua; Vaman, Diana

2017-01-01

A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.

q-deformed charged fermion coherent states and SU(3) charged, Hyper-charged fermion coherent states

International Nuclear Information System (INIS)

Hao Sanru; Li Guanghua; Long Junyan

1994-01-01

By virtue of the algebra of the q-deformed fermion oscillators, the q-deformed charged fermion coherent states and SU(3) charged, hyper-charged fermion coherent states are discussed. The explicit forms of the two kinds of coherent states mentioned above are obtained by making use of the completeness of base vectors in the q-fermion Fock space. By comparing the q-deformed results with the ordinary results, it is found that the q-deformed charged fermion coherent states and SU(3) charged, hyper-charged fermion coherent states are automatically reduced to the ordinary charged fermion coherent states and SU(3) charged hyper-charged fermion coherent states if the deformed parameter q→1

Fermionic vacuum polarization by a cylindrical boundary in the cosmic string spacetime

International Nuclear Information System (INIS)

Bezerra de Mello, E. R.; Bezerra, V. B.; Saharian, A. A.; Tarloyan, A. S.

2008-01-01

The vacuum expectation values of the energy-momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode sums a variant of the generalized Abel-Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.

Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions

OpenAIRE

Chandrasekharan, Shailesh; Li, Anyi

2010-01-01

We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and th...

Fermion number in supersymmetric models

International Nuclear Information System (INIS)

Mainland, G.B.; Tanaka, K.

1975-01-01

The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.)

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2018-01-01

textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2017-01-01

textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in

Observables and transformation properties of fermions and parafermions constructed in terms of bosons

International Nuclear Information System (INIS)

Kalnay, A.J.; Kademova, K.V.

1975-01-01

Further to work previously reported (Kalnay. MacCotrina and Kademova. Int. J. Theor. Phys.; 7:9 (1973)) in which it was shown how the quantum Fermi or para-Fermi commutation rules of fields could be reproduced in terms of functions of Bose fields and of part 1 of the present work (Kalnay and Kademova. Int. J. Theor. Phys.; 12:141 (1975)), the same concepts are here utilized for the Bose representation of transformation laws. It is apparent that the Bose representation does not introduce conflict between the tensor transformation laws of bosons and the spinor laws of fermions and parafermions. (U.K.)

Tensor rank is not multiplicative under the tensor product

OpenAIRE

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2017-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2018-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2016-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new

Fermion cluster algorithms

International Nuclear Information System (INIS)

Chandrasekharan, Shailesh

2000-01-01

Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion world lines. This solution leads to the possibility of designing fermion cluster algorithms in certain cases. Using the example of free non-relativistic fermions we discuss the ideas underlying the algorithm

Tensor rank is not multiplicative under the tensor product

DEFF Research Database (Denmark)

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2018-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...

On the unboundedness of control operators for bilinear systems ...

African Journals Online (AJOL)

The aim of this work is to study the classes of unbounded linear control operators which ensure the existence and uniqueness of the mild and strong solutions of certain bilinear control systems. By an abstract approach, similar to that adopted by Weiss [18], we obtain a connection between these classes and those ...

Second order statistics of bilinear forms of robust scatter estimators

KAUST Repository

Kammoun, Abla; Couillet, Romain; Pascal, Fré dé ric

2015-01-01

. In particular, we analyze the fluctuations of bilinear forms of the robust shrinkage estimator of covariance matrix. We show that this result can be leveraged in order to improve the design of robust detection methods. As an example, we provide an improved

Non-perturbative renormalization in coordinate space for N{sub f}=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action

Energy Technology Data Exchange (ETDEWEB)

Cichy, Krzysztof [DESY, Zeuthen (Germany). NIC; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [DESY, Zeuthen (Germany). NIC; Korcyl, Piotr [DESY, Zeuthen (Germany). NIC; Jagiellonian Univ., Krakow (Poland). M. Smoluchowski Inst. of Physics

2012-07-15

We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N{sub f}=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)

The sample ACF of a simple bilinear process

NARCIS (Netherlands)

Basrak, B; Davis, RA; Mikosch, T

1999-01-01

We consider a simple bilinear process X-t = aX(t-1) + bX(t-1)Z(t-1) +Z(t), where (Z(t)) is a sequence of iid N(0, 1) random variables. It follows from a result by Kesten (1973, Acta Math. 131, 207-248) that X-t has a distribution with regularly varying tails of index alpha > 0 provided the equation

Bilinear reduced order approximate model of parabolic distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed

2015-07-01

This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the gaussian interpolation has been studied.

2-fermion and 4-fermion production at LEP2

CERN Document Server

van Vulpen, Ivo B

2000-01-01

We present the measurements on 2-fermion and 4-fermion production in e + e - collisions at centre-of-mass energies ranging from 192 to 202 Ge V as collected by the 4 LEP experiments in 1999. For processes with 2-fermions in the final state we present both production cross sections and asymmetries for event samples at low and high effective centre-of-mass energies, where the latter process is sensitive to possible contributions from various non-SM physics, like contact interactions or Z' exchange, and can therefore be used to set limits on parameters in those models. We also report on the measured cross sections for a subset of processes leading to 4 fermions in the final state: pair production of heavy vector bosons w+w- (NC03) and ZZ (NC02) followed by single-W production. A measurement of the leptonic branching ratio of the W-boson is used to extract information on IV c• I

Fermions and non-Abelian vortex

International Nuclear Information System (INIS)

Mello, E.R.B. de.

1986-01-01

Some aspectos of the fermion-non-Abelian vortex system are discussed. It is shown that this system presents properties analogous to the fermion-non-Abelian magnetic monopole one. But, differrently from the fermion-monopole case, this system does not present fermion condensate V = 0. (Author) [pt

Exchange mechanisms for single photo- and electroproduction using the dual fermion model

International Nuclear Information System (INIS)

Becker, L.; Weigt, G.

1976-01-01

Single pion real and virtual photoproduction data are compared with phenomenological dual fermion amplitudes, which were previously applied to quasi-two body vector and tensor meson production. The similar structures of the photon and the corresponding vector meson data (in the s-channel helicity system) such as spikes and dips, usually described by Regge pole/Regge cut interferences, are reproduced by the dual Born amplitudes. Predictions of the model for the differential cross sections, in particular their parts for natural and unnatural spin-parity t-channel exchanges as well as their mass dependence, and photon and target asymmetries are in reasonable agreement with the experimental data. (author)

BILAM: a composite laminate failure-analysis code using bilinear stress-strain approximations

Energy Technology Data Exchange (ETDEWEB)

McLaughlin, P.V. Jr.; Dasgupta, A.; Chun, Y.W.

1980-10-01

The BILAM code which uses constant strain laminate analysis to generate in-plane load/deformation or stress/strain history of composite laminates to the point of laminate failure is described. The program uses bilinear stress-strain curves to model layer stress-strain behavior. Composite laminates are used for flywheels. The use of this computer code will help to develop data on the behavior of fiber composite materials which can be used by flywheel designers. In this program the stress-strain curves are modelled by assuming linear response in axial tension while using bilinear approximations (2 linear segments) for stress-strain response to axial compressive, transverse tensile, transverse compressive and axial shear loadings. It should be noted that the program attempts to empirically simulate the effects of the phenomena which cause nonlinear stress-strain behavior, instead of mathematically modelling the micromechanics involved. This code, therefore, performs a bilinear laminate analysis, and, in conjunction with several user-defined failure interaction criteria, is designed to provide sequential information on all layer failures up to and including the first fiber failure. The modus operandi is described. Code BILAM can be used to: predict the load-deformation/stress-strain behavior of a composite laminate subjected to a given combination of in-plane loads, and make analytical predictions of laminate strength.

Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

Science.gov (United States)

Taniguchi, Yusuke; Ejiri, Shinji; Kanaya, Kazuyuki; Kitazawa, Masakiyo; Suzuki, Asobu; Suzuki, Hiroshi; Umeda, Takashi

2018-03-01

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Dynamical FLIC fermions

International Nuclear Information System (INIS)

Kamleh, W.; Leinweber, D.B.; Williams, A.G.

2004-01-01

The use of APE smearing or other blocking techniques in fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard. Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants

A Review of Tensors and Tensor Signal Processing

Science.gov (United States)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Superstrings fermionic solutions

International Nuclear Information System (INIS)

Rausch de Traubenberg, M.

1990-06-01

The solutions proposed by the superstring theory are classified and compared. In order to obtain some of the equivalences, the demonstration is based on the coincidence of the excitation spectrum and the quantum numbers from different states. The fermionic representation of the heterotical strings is discussed. The conformal invariance and the supersymmetric results extended to two dimensions are investigated. Concerning the fermionic strings, the formalism and a phenomenological solution involving three families of quarks, chiral leptons and leptons from the E 6 gauge group are presented. The equivalence between real and complex fermions is discussed. The similarity between some of the solutions of the Wess-Zumino-Witten model and the orbifolds is considered. The formal calculation program developed for reproducing the theory's low energy spectra, in the fermionic string formalism is given [fr

The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre

Energy Technology Data Exchange (ETDEWEB)

Farsad, Vanda

2017-06-14

This thesis is concerned with ''N pairs of symplectic fermions'' which are examples of logarithmic conformal field theories in two dimensions. The mathematical language of two-dimensional conformal field theories (on Riemannian surfaces of genus zero) are vertex operator algebras. The representation category of the even part of the symplectic fermion vertex operator super-algebra Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category. This determines an isomorphism of projective representations between two SL(2,Z)-actions associated to V{sub ev}. The first action is obtained by modular transformations on the space of so-called pseudo-trace functions of a vertex operator algebra. For V{sub ev} this was developed by A.M.Gaberdiel and I. Runkel. For the action one uses that Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category and thus carries a projective SL(2,Z)-action on a certain Hom-space [Ly1,Ly2,KL]. To do so we calculate the SL(2,Z)-action on the representation category of a general factorisable quasi-Hopf algebras. Then we show that Rep V{sub ev} is conjecturally ribbon equivalent to Rep Q, for Q a factorisable quasi-Hopf algebra, and calculate the SL(2,Z)-action explicitly on Rep Q. The result is that the two SL(2,Z)-action indeed agree. This poses the first example of such comparison for logarithmic conformal field theories.

Control configuration selection for bilinear systems via generalised Hankel interaction index array

DEFF Research Database (Denmark)

Shaker, Hamid Reza; Tahavori, Maryamsadat

2015-01-01

configuration selection. It is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control. In this paper the problem of control configuration selection for multiple-input and multiple-output (MIMO) bilinear processes is addressed. First...... way, an iterative method for solving the generalised Sylvester equation is proposed. The generalised cross-gramian is used to form the generalised Hankel interaction index array. The generalised Hankel interaction index array is used for control configuration selection of MIMO bilinear processes. Most......Decentralised and partially decentralised control strategies are very popular in practice. To come up with a suitable decentralised or partially decentralised control structure, it is important to select the appropriate input and output pairs for control design. This procedure is called control...

Fermion-fermion scattering in quantum field theory with superconducting circuits.

Science.gov (United States)

García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E

2015-02-20

We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations.

Smooth surfaces from bilinear patches: Discrete affine minimal surfaces

KAUST Repository

Käferböck, Florian

2013-06-01

Motivated by applications in freeform architecture, we study surfaces which are composed of smoothly joined bilinear patches. These surfaces turn out to be discrete versions of negatively curved affine minimal surfaces and share many properties with their classical smooth counterparts. We present computational design approaches and study special cases which should be interesting for the architectural application. 2013 Elsevier B.V.

High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n{sub f} = 4 Wilson fermions

Energy Technology Data Exchange (ETDEWEB)

Brambilla, M.; Di Renzo, F. [Universita di Parma (Italy); INFN, Gruppo Collegato di Parma, Dipartimento di Fisica e Scienze della Terra, Parma (Italy); Hasegawa, M. [Universita di Parma (Italy); Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); INFN, Gruppo Collegato di Parma, Dipartimento di Fisica e Scienze della Terra, Parma (Italy)

2014-07-15

This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main points of interest are results for the regularization defined by the Iwasaki gauge action and n{sub f} Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for twisted mass QCD: being defined in the chiral limit, the renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of boosted perturbation theory and the disentanglement of irrelevant and finite-volume contributions. Discussing these issues we consider not only the new results of this paper, but also those for the regularization defined by the tree-level Symanzik improved gauge action and n{sub f} Wilson fermions, which we presented in a recent paper of ours. We finally comment on the extent to which the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme. (orig.)

Novikov algebras with associative bilinear forms

Energy Technology Data Exchange (ETDEWEB)

Zhu Fuhai; Chen Zhiqi [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)

2007-11-23

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

Directory of Open Access Journals (Sweden)

Taniguchi Yusuke

2018-01-01

Full Text Available We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

Lattice degeneracies of fermions

International Nuclear Information System (INIS)

Raszillier, H.

1983-10-01

We present a detailed description of the minimal degeneracies of geometric (Kaehler) fermions on all the lattices of maximal symmetries in n = 1, ..., 4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ''naive'' fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras. (orig.)

Stress-tensor commutators and Schwinger terms in singleton theories

International Nuclear Information System (INIS)

Bergshoeff, E.; Sezgin, E.; Tanii, Y.

1989-06-01

We compute the commutators of the regularized quantum stress-tensor of singleton theories formulated on the boundary of a (p + 2)-dimensional anti de Sitter space (AdS p+2 ). (These are superconformal field theories on S p x S 1 ). We find that the algebra is not closed except in the case of AdS 3 . It does contain, however, the finite dimensional AdS p+2 algebra SO(p + 1,2). We also find divergent, field dependent as well as field independent Schwinger terms (i.e. the central extensions), which, however, do not lead to anomalies in the algebra of the AdS charges. We also give a simple derivation of the two-point functions for bosonic and fermionic singletons. (author). 15 refs

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

2015-01-01

Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085

Fermion bag solutions to some sign problems in four-fermion field theories

International Nuclear Information System (INIS)

Li, Anyi

2013-01-01

Lattice four-fermion models containing N flavors of staggered fermions, that are invariant under Z 2 and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. In this talk, we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.

Fermion bag solutions to some sign problems in four-fermion field theories

Science.gov (United States)

Li, Anyi

2013-04-01

Lattice four-fermion models containing N flavors of staggered fermions, that are invariant under Z2 and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. In this talk, we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.

From pure spinors to quantum physics and to some classical field equations like Maxwell's and gravitational

International Nuclear Information System (INIS)

Budinich, Paolo

2009-03-01

In a previous paper we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 components spinors. Here we proceed along that path proposing, this time, a symmetric tensor, quadrilinear in simple spinors, as a candidate for the symmetric tensor of general relativity. The procedure resembles closely that in which one builds bilinearly from simple spinors an asymmetric electromagnetic tensor, from which easily descend Maxwell's equations and the photon can be seen as a bilinear combination of neutrinos. Here Lorentzian spaces result compact, building up spheres, where hopefully the problems of the Standard Model could be solved. (author)

MSW-resonant fermion mixing during reheating

Science.gov (United States)

Kanai, Tsuneto; Tsujikawa, Shinji

2003-10-01

We study the dynamics of reheating in which an inflaton field couples two flavor fermions through Yukawa-couplings. When two fermions have a mixing term with a constant coupling, we show that the Mikheyev-Smirnov-Wolfenstein (MSW)-type resonance emerges due to a time-dependent background in addition to the standard fermion creation via parametric resonance. This MSW resonance not only alters the number densities of fermions generated by a preheating process but also can lead to the larger energy transfer from the inflaton to fermions. Our mechanism can provide additional source terms for the creation of superheavy fermions which may be relevant for the leptogenesis scenario.

MSW-resonant fermion mixing during reheating

International Nuclear Information System (INIS)

Kanai, Tsuneto; Tsujikawa, Shinji

2003-01-01

We study the dynamics of reheating in which an inflaton field couples two flavor fermions through Yukawa-couplings. When two fermions have a mixing term with a constant coupling, we show that the Mikheyev-Smirnov-Wolfenstein (MSW)-type resonance emerges due to a time-dependent background in addition to the standard fermion creation via parametric resonance. This MSW resonance not only alters the number densities of fermions generated by a preheating process but also can lead to the larger energy transfer from the inflaton to fermions. Our mechanism can provide additional source terms for the creation of superheavy fermions which may be relevant for the leptogenesis scenario

Spectral density of oscillator with bilinear stiffness and white noise excitation

DEFF Research Database (Denmark)

Rüdinger, Finn; Krenk, Steen

2003-01-01

The power spectral density of an oscillator with bilinear stiffness excited by Gaussian white noise is considered. A method originally proposed by Krenk and Roberts [J Appl Mech 66 (1999) 225] relying on slowly changing energy for lightly damped systems is applied. In this method an approximate...

Optimization and Control of Bilinear Systems Theory, Algorithms, and Applications

CERN Document Server

Pardalos, Panos M

2008-01-01

Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science

On the bilinear covariants associated to mass dimension one spinors

Energy Technology Data Exchange (ETDEWEB)

Silva, J.M.H. da; Villalobos, C.H.C.; Rogerio, R.J.B. [DFQ, UNESP, Guaratingueta, SP (Brazil); Scatena, E. [Universidade Federal de Santa Catarina-CEE, Blumenau, SC (Brazil)

2016-10-15

In this paper we approach the issue of Clifford algebra basis deformation, allowing for bilinear covariants associated to Elko spinors which satisfy the Fierz-Pauli-Kofink identities. We present a complete analysis of covariance, taking into account the involved dual structure associated to Elko spinors. Moreover, the possible generalizations to the recently presented new dual structure are performed. (orig.)

Smooth surfaces from rational bilinear patches

KAUST Repository

Shi, Ling

2014-01-01

Smooth freeform skins from simple panels constitute a challenging topic arising in contemporary architecture. We contribute to this problem area by showing how to approximate a negatively curved surface by smoothly joined rational bilinear patches. The approximation problem is solved with help of a new computational approach to the hyperbolic nets of Huhnen-Venedey and Rörig and optimization algorithms based on it. We also discuss its limits which lie in the topology of the input surface. Finally, freeform deformations based on Darboux transformations are used to generate smooth surfaces from smoothly joined Darboux cyclide patches; in this way we eliminate the restriction to surfaces with negative Gaussian curvature. © 2013 Elsevier B.V.

The investigation of the non-orthogonal basis expansion method for a three-fermion system

International Nuclear Information System (INIS)

Baoqiu Chen; Kentucky Univ., Lexington, KY

1992-01-01

In this paper, the non-orthogonal basis expansion method has been extended to solve a three-fermion system. The radial wavefunction of such a system is expanded in terms of a non-orthogonal Gaussian basis. All matrix elements of the Hamiltonian, including the central, tensor and spin-orbit potentials are derived in analytical forms. The new method simplifies the three-body system calculations, which are usually rather tedious by other methods. The method can be used to calculate energies for both the ground state and low excited states and has been used further to investigate the other nuclear properties of a three-body system such as Λ 3 H. (Author)

Bilinear Time-frequency Analysis for Lamb Wave Signal Detected by Electromagnetic Acoustic Transducer

Science.gov (United States)

Sun, Wenxiu; Liu, Guoqiang; Xia, Hui; Xia, Zhengwu

2018-03-01

Accurate acquisition of the detection signal travel time plays a very important role in cross-hole tomography. The experimental platform of aluminum plate under the perpendicular magnetic field is established and the bilinear time-frequency analysis methods, Wigner-Ville Distribution (WVD) and the pseudo-Wigner-Ville distribution (PWVD), are applied to analyse the Lamb wave signals detected by electromagnetic acoustic transducer (EMAT). By extracting the same frequency component of the time-frequency spectrum as the excitation frequency, the travel time information can be obtained. In comparison with traditional linear time-frequency analysis method such as short-time Fourier transform (STFT), the bilinear time-frequency analysis method PWVD is more appropriate in extracting travel time and recognizing patterns of Lamb wave.

Fermions from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p τ amounts to a rotation of the wave function q τ (t)=±√(p τ (t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

An SU(2) x SU(2) symmetric Higgs-Fermion model with staggered fermions

International Nuclear Information System (INIS)

Berlin, J.; Heller, U.M.

1991-01-01

We have simulated on SU(2)xSU(2) symmetric Higgs-Fermion model with a four component scalar field coupled with a Yukawa type coupling to two flavours of staggered fermions. The results show two qualitatively different behaviours in the broken phase. One for weak coupling where the fermion masses obey the perturbative tree level relation M F =y , and one for strong coupling where the behaviour agrees with a 1/d expansion. (orig.)

Feynman rules for fermion-number-violating interactions

International Nuclear Information System (INIS)

Denner, A.; Eck, H.; Hahn, O.; Kueblbeck, J.

1992-01-01

We present simple algorithmic Feynman rules for fermion-number-violating interactions. They do not involve explicit charge-conjugation matrices and resemble closely the familiar rules for Dirac fermions. We insist on a fermion flow through the graphs along fermion lines and get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions. We only need the familiar Dirac propagator and fewer vertices than in the usual treatment of fermion-number-violating interactions. (orig.)

More on random-lattice fermions

International Nuclear Information System (INIS)

Kieu, T.D.; Institute for Advanced Study, Princeton, NJ; Markham, J.F.; Paranavitane, C.B.

1995-01-01

The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sufficient condition to remove the fermion doublers. 8 refs., 3 figs

Fermion number non-conservation and cold neutral fermionic matter in (V-A) gauge theories

International Nuclear Information System (INIS)

Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Tokarev, V.F.

1987-01-01

It is shown that in four-dimensional abelian (V-A) theories, the ground state of cold neutral fermionic matter is an anomalous state containing domains of abnormal phase surrounded by the normal vacuum. Inside these domains, there exists a gauge field condensate which makes real fermions disappear both inside and outside the domains. In non-abelian theories, the abnormal matter is unstable in its turn, and the system rolls back down into the normal state with a small number of fermions above the topologically non-trivial vacuum. Thus, in several non-abelian gauge theories, the fermion number density of cold neutral matter cannot exceed some critical value. (orig.)

SSB of Scale Symmetry, Fermion Families and Quintessence without the Long-Range Force Problem

Science.gov (United States)

Guendelman, E. I.; Kaganovich, A. B.

We study a scale-invariant two measures theory where a dilaton field φ has no explicit potentials. The scale transformations include the translation of a dilaton φ-->φ+ const. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, the nonlinear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. As examples, two different possibilities for the choice of the dimensionless parameters are presented where the theory permits to get interesting cosmological results. For the first choice, the theory has standard scaling solutions for φ usually used in the context of the quintessential scenario. For the second choice, the theory allows three different solutions, one of which is a scaling solution with equation of state pφ=wρφ where w is predicted to be restricted by -1fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, the energy-momentum tensor is canonical and the ``fifth force'' is absent. For the third type of particles, a fermionic self-interaction appears as a result of SSB of scale invariance.

Ultracold fermion race is on

International Nuclear Information System (INIS)

Hulet, R.

1999-01-01

At the quantum level, particles behave very differently depending on whether their spin angular momentum is an integer or a half-integer. Half-integer spin particles are known as fermions, and include all the constituents of atoms: electrons, protons and neutrons. Bosons, on the other hand, are particles with integer spin, such as photons. Atoms are fermions if they are composed of an odd number of particles, like helium-3 or lithium-6. If they have an even number of constituents, like hydrogen, helium-4 or lithium-7, they are known as bosons. Fermions and bosons behave in profoundly different ways under certain conditions, especially at low temperatures. Four years ago, physicists created a Bose condensate, a quantum degenerate gas of bosons. Now the race is on to do the same with fermions. Deborah Jin's group at the US National Institute of Standards and Technology (NIST) and the University of Colorado has cooled a fermion gas to the lowest temperature yet (B DeMarco 1999 Phys. Rev. Lett. 82 4208). And John Thomas and co-workers at Duke University have set a new record for the length of time that fermions can be trapped using lasers (K O'Hara 1999 Phys. Rev. Lett. 82 4204). In this article the author describes the latest advances in the race to create a quantum degenerate gas of fermions. (UK)

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-07-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.

Fermion masses and multiplicity

International Nuclear Information System (INIS)

Ramond, P.

1986-01-01

A general survey and analysis of fermion masses is presented in terms of both the known low energy gauge structure and of the simplest GUT structure. The replication of fermion families is discussed in the context of possible family group structures. Sample family gauge groups are presented in the cases of three and four chiral families, using ABJ and Witten anomalies to restrict the maximal gauged family group. The possible relevance of the family group to the fermion mass hierarchy is discussed in the context of various models. (author)

Mirror fermions and cosmology

International Nuclear Information System (INIS)

Senjanovic, G.; Virginia Polytechnic Inst. and State Univ., Blacksburg

1984-07-01

Extended supersymmetry, Kaluza-Klein theory and family unification all suggest the existence of mirror fermions, with same quantum numbers but opposite helicities from ordinary fermions. The laboratory and especially cosmological implications of such particles are reviewed and summarized. (author)

Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

Science.gov (United States)

Li, Wei; Liu, Chunlei

2013-10-01

Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.

Fermion bag solutions to some unsolved sign problems

Science.gov (United States)

Li, Anyi; Chandrasekharan, Shailesh

2012-03-01

Some interesting lattice four-fermion models containing N flavors of staggered fermions with Z2 and U(1) chiral symmetries suffer from sign problems in the auxiliary field approach. Earlier calculations have either ignored these sign problems or have circumvented them by adding conjugate fermion fields which changes the model. In this talk we show that the recently proposed fermion bag approach solves these sign problems. The basic idea of the new approach is to collect unpaired fermionic degrees of freedom inside a fermion bag. A resummation of all fermion world lines inside the bag is then sufficient to solve the sign problems. The fermion bag approach provides new opportunities to solve in these ``unsolved'' four-fermion models in the chiral limit efficiently.

Killing tensors and conformal Killing tensors from conformal Killing vectors

International Nuclear Information System (INIS)

Rani, Raffaele; Edgar, S Brian; Barnes, Alan

2003-01-01

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors

Tensors for physics

CERN Document Server

Hess, Siegfried

2015-01-01

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...

Renormalization of fermion mixing

International Nuclear Information System (INIS)

Schiopu, R.

2007-01-01

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

Renormalization of fermion mixing

Energy Technology Data Exchange (ETDEWEB)

Schiopu, R.

2007-05-11

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

Excited fermions

International Nuclear Information System (INIS)

Boudjema, F.; Djouadi, A.; Kneur, J.L.

1992-01-01

The production of excited fermions with mass above 100 GeV is considered. f→Vf (1) decay widths are calculated where V=γ, Z or W. Excited fermion pair production in e + e - annihilation and in γγ collisions, and single production in e + e - annihilation, eγ and γγ collisions is also discussed. Cross sections are calculated for all these cases. The discovery potential of the NLC at 500 GeV is compared with that of other colliders. (K.A.) 15 refs., 5 figs., 2 tabs

Solving the AKNS Hierarchy by Its Bilinear Form: Generalized Double Wronskian Solutions

International Nuclear Information System (INIS)

Yin Fumei; Sun Yepeng; Cai Fuqing; Chen Dengyuan

2008-01-01

Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.

Half-unit weighted bilinear algorithm for image contrast enhancement in capsule endoscopy

Science.gov (United States)

Rukundo, Olivier

2018-04-01

This paper proposes a novel enhancement method based exclusively on the bilinear interpolation algorithm for capsule endoscopy images. The proposed method does not convert the original RBG image components to HSV or any other color space or model; instead, it processes directly RGB components. In each component, a group of four adjacent pixels and half-unit weight in the bilinear weighting function are used to calculate the average pixel value, identical for each pixel in that particular group. After calculations, groups of identical pixels are overlapped successively in horizontal and vertical directions to achieve a preliminary-enhanced image. The final-enhanced image is achieved by halving the sum of the original and preliminary-enhanced image pixels. Quantitative and qualitative experiments were conducted focusing on pairwise comparisons between original and enhanced images. Final-enhanced images have generally the best diagnostic quality and gave more details about the visibility of vessels and structures in capsule endoscopy images.

How real are composite fermions?

International Nuclear Information System (INIS)

Kang, W.; Stormer, H.L.; Pfeiffer, L.N.; Baldwin, K.W.; West, K.W.

1995-01-01

A new picture of fractional quantum Hall effect (FQHE) in terms of a novel particle called composite fermion has emerged recently. A composite fermion is a composite of two flux quanta which are effectively bound to an electron as a result of electron-electron interaction. A system of electrons at half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field with a distinct Fermi surface. The FQHE is then viewed as the integral quantum Hall effect of composite fermions away from half-filling. In order to test for these new particles, we have studied transport of anti-dot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the anti-dot lattice. At half-filling we observe the same dimensional resonances. This establishes the ''semi-classical'' behavior of composite fermions. (orig.)

BILINEAR SYSTEM AS A MODELLING FRAMEWORK FOR ANALYSIS OF MICROALGAL GROWTH

Czech Academy of Sciences Publication Activity Database

Papáček, Š.; Čelikovský, Sergej; Štys, D.; Ruiz León, J.

2007-01-01

Roč. 43, č. 1 (2007), s. 1-20 ISSN 0023-5954 R&D Projects: GA ČR GA102/05/0011 Institutional research plan: CEZ:AV0Z10750506 Keywords : bilinear system * model of photosynthetic factory * microalgae * light/dark cycles * flashing light experiments Subject RIV: BC - Control Systems Theory Impact factor: 0.552, year: 2007

Bilinear Convolutional Neural Networks for Fine-grained Visual Recognition.

Science.gov (United States)

Lin, Tsung-Yu; RoyChowdhury, Aruni; Maji, Subhransu

2017-07-04

We present a simple and effective architecture for fine-grained recognition called Bilinear Convolutional Neural Networks (B-CNNs). These networks represent an image as a pooled outer product of features derived from two CNNs and capture localized feature interactions in a translationally invariant manner. B-CNNs are related to orderless texture representations built on deep features but can be trained in an end-to-end manner. Our most accurate model obtains 84.1%, 79.4%, 84.5% and 91.3% per-image accuracy on the Caltech-UCSD birds [66], NABirds [63], FGVC aircraft [42], and Stanford cars [33] dataset respectively and runs at 30 frames-per-second on a NVIDIA Titan X GPU. We then present a systematic analysis of these networks and show that (1) the bilinear features are highly redundant and can be reduced by an order of magnitude in size without significant loss in accuracy, (2) are also effective for other image classification tasks such as texture and scene recognition, and (3) can be trained from scratch on the ImageNet dataset offering consistent improvements over the baseline architecture. Finally, we present visualizations of these models on various datasets using top activations of neural units and gradient-based inversion techniques. The source code for the complete system is available at http://vis-www.cs.umass.edu/bcnn.

Theoretical studies of strongly correlated fermions

Energy Technology Data Exchange (ETDEWEB)

Logan, D [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

1997-04-01

Strongly correlated fermions are investigated. An understanding of strongly correlated fermions underpins a diverse range of phenomena such as metal-insulator transitions, high-temperature superconductivity, magnetic impurity problems and the properties of heavy-fermion systems, in all of which local moments play an important role. (author).

Fermion-induced quantum critical points.

Science.gov (United States)

Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

2017-08-22

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

Science.gov (United States)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

International Nuclear Information System (INIS)

Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

2011-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

International Nuclear Information System (INIS)

Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

2010-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

2010-12-22

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

Bootstrapping 3D fermions

Energy Technology Data Exchange (ETDEWEB)

Iliesiu, Luca [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Kos, Filip; Poland, David [Department of Physics, Yale University, New Haven, CT 06520 (United States); Pufu, Silviu S. [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Simmons-Duffin, David [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States); Yacoby, Ran [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States)

2016-03-17

We study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ×ψ OPE, and also on the central charge C{sub T}. We observe features in our bounds that coincide with scaling dimensions in the Gross-Neveu models at large N. We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.

Phase space methods for Majorana fermions

Science.gov (United States)

Rushin Joseph, Ria; Rosales-Zárate, Laura E. C.; Drummond, Peter D.

2018-06-01

Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes. This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects. We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker–Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators. The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker–Planck and stochastic equation form, including dissipation through particle losses.

Dynamical fermions in lattice quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Szabo, Kalman

2007-07-01

The thesis presentS results in Quantum Chromo Dynamics (QCD) with dynamical lattice fermions. The topological susceptibilty in QCD is determined, the calculations are carried out with dynamical overlap fermions. The most important properties of the quark-gluon plasma phase of QCD are studied, for which dynamical staggered fermions are used. (orig.)

Dynamical fermions in lattice quantum chromodynamics

International Nuclear Information System (INIS)

Szabo, Kalman

2007-01-01

The thesis presentS results in Quantum Chromo Dynamics (QCD) with dynamical lattice fermions. The topological susceptibilty in QCD is determined, the calculations are carried out with dynamical overlap fermions. The most important properties of the quark-gluon plasma phase of QCD are studied, for which dynamical staggered fermions are used. (orig.)

Gauge invariance and fermion mass dimensions

International Nuclear Information System (INIS)

Elias, V.

1979-05-01

Renormalization-group equation fermion mass dimensions are shown to be gauge dependent in gauge theories possessing non-vector couplings of gauge bosons to fermions. However, the ratios of running fermion masses are explicitly shown to be gauge invariant in the SU(5) and SU(2) x U(1) examples of such theories. (author)

Fermion condensation and gapped domain walls in topological orders

Energy Technology Data Exchange (ETDEWEB)

Wan, Yidun [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing 210093 (China); Perimeter Institute for Theoretical Physics,Waterloo N2L 2Y5, Ontario (Canada); Wang, Chenjie [Perimeter Institute for Theoretical Physics,Waterloo N2L 2Y5, Ontario (Canada)

2017-03-31

We study fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation may be realized as gapped domain walls between bosonic and fermionic topological orders, which may be thought of as real-space phase transitions from bosonic to fermionic topological orders. This picture generalizes the previous idea of understanding boson condensation as gapped domain walls between bosonic topological orders. While simple-current fermion condensation was considered before, we systematically study general fermion condensation and show that it obeys a Hierarchy Principle: a general fermion condensation can always be decomposed into a boson condensation followed by a minimal fermion condensation. The latter involves only a single self-fermion that is its own anti-particle and that has unit quantum dimension. We develop the rules of minimal fermion condensation, which together with the known rules of boson condensation, provides a full set of rules for general fermion condensation.

Fermionic Markov Chains

OpenAIRE

Fannes, Mark; Wouters, Jeroen

2012-01-01

We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.

Fermions and bosons : a 'spinless' approach

International Nuclear Information System (INIS)

Oliveira, P.M.C. de; Ribeiro, S.C.

1980-07-01

The fundamental difference between fermions and bosons is presented. The treatment used is based only on indistinguishability and its related implications on interference, with no mention to spin. Comparison between indistinguishable (fermions or bosons) and distinguishable identical particles are also made, yielding the enhancement (bosons) or inhibition (fermions) factors which determine the quantum distribution equations. (Author) [pt

The dilute spin-one Ising model with both bilinear and biquadratic exchange interactions

International Nuclear Information System (INIS)

Saber, M.

1987-08-01

The influence of bond and site dilution on the two-dimensional spin-one Ising model on a honeycomb lattice is investigated. Temperature-concentration phase diagrams for fixed values of the ratio of bilinear and biquadratic exchange interactions are determined. (author). 7 refs, 3 figs

Fermion masses from dimensional reduction

International Nuclear Information System (INIS)

Kapetanakis, D.; Zoupanos, G.

1990-01-01

We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.)

Fermion masses from dimensional reduction

Energy Technology Data Exchange (ETDEWEB)

Kapetanakis, D. (National Research Centre for the Physical Sciences Democritos, Athens (Greece)); Zoupanos, G. (European Organization for Nuclear Research, Geneva (Switzerland))

1990-10-11

We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.).

Phantom cosmologies and fermions

International Nuclear Information System (INIS)

Chimento, Luis P; Forte, Monica; Devecchi, Fernando P; Kremer, Gilberto M

2008-01-01

Form invariance transformations can be used for constructing phantom cosmologies starting with conventional cosmological models. In this work we reconsider the scalar field case and extend the discussion to fermionic fields, where the 'phantomization' process exhibits a new class of possible accelerated regimes. As an application we analyze the cosmological constant group for a fermionic seed fluid

Null-plane quantization of fermions

International Nuclear Information System (INIS)

Mustaki, D.

1990-01-01

Massive Dirac fermions are canonically quantized on the null plane using the Dirac-Bergmann algorithm. The procedure is carried out in the framework of quantum electrodynamics as an illustration of a rigorous treatment of interacting fermion fields

Improved lattice fermion action for heavy quarks

International Nuclear Information System (INIS)

Cho, Yong-Gwi; Hashimoto, Shoji; Jüttner, Andreas; Kaneko, Takashi; Marinkovic, Marina; Noaki, Jun-Ichi; Tsang, Justus Tobias

2015-01-01

We develop an improved lattice action for heavy quarks based on Brillouin-type fermions, that have excellent energy-momentum dispersion relation. The leading discretization errors of O(a) and O(a"2) are eliminated at tree-level. We carry out a scaling study of this improved Brillouin fermion action on quenched lattices by calculating the charmonium energy-momentum dispersion relation and hyperfine splitting. We present a comparison to standard Wilson fermions and domain-wall fermions.

The energy–momentum tensor(s in classical gauge theories

Directory of Open Access Journals (Sweden)

Daniel N. Blaschke

2016-11-01

Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

Fermions on the electroweak string

CERN Document Server

Moreno, J M; Quirós, Mariano; Moreno, J M; Oaknin, D H; Quiros, M

1995-01-01

We construct a simple class of exact solutions of the electroweak theory including the naked Z--string and fermion fields. It consists in the Z--string configuration (\\phi,Z_\\theta), the {\\it time} and z components of the neutral gauge bosons (Z_{0,3},A_{0,3}) and a fermion condensate (lepton or quark) zero mode. The Z--string is not altered (no feed back from the rest of fields on the Z--string) while fermion condensates are zero modes of the Dirac equation in the presence of the Z--string background (no feed back from the {\\it time} and z components of the neutral gauge bosons on the fermion fields). For the case of the n--vortex Z--string the number of zero modes found for charged leptons and quarks is (according to previous results by Jackiw and Rossi) equal to |n|, while for (massless) neutrinos is |n|-1. The presence of fermion fields in its core make the obtained configuration a superconducting string, but their presence (as well as that of Z_{0,3},A_{0,3}) does not enhance the stability of the Z--stri...

Low energy fermion number violation

International Nuclear Information System (INIS)

Peccei, R.D.

1989-01-01

After a brief aside on charge quantization in the standard electroweak theory, I concentrate on various aspects of anomaly induced fermion number violation in the standard model. A critical analysis of the role of sphalerons for the universe's baryon asymmetry is presented and the importance of calculating directly fermion number violating Green's functions is stressed. A physical interpretation of the recent observation of Ringwald, that coherent effects in the electroweak theory lead to catastrophic fermion number violation at 100 TeV, is discussed. Possible quantum effects which might spoil this semi-classical picture are examined

Efficient tensor completion for color image and video recovery: Low-rank tensor train

OpenAIRE

Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.

2016-01-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...

Optimal Bilinear Control of Gross--Pitaevskii Equations

KAUST Repository

Hintermü ller, Michael; Marahrens, Daniel; Markowich, Peter A.; Sparber, Christof

2013-01-01

A mathematical framework for optimal bilinear control of nonlinear Schrödinger equations of Gross--Pitaevskii type arising in the description of Bose--Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects. In particular, the cost induced by the physical workload over the control process is taken into account rather than the often used L^2- or H^1-norms for the cost of the control action. Well-posedness of the problem and existence of an optimal control are proved. In addition, the first order optimality system is rigorously derived. Also a numerical solution method is proposed, which is based on a Newton-type iteration, and used to solve several coherent quantum control problems.

On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action

Science.gov (United States)

Chekhov, L. O.; Mazzocco, M.

2017-12-01

Let \\mathscr A be the space of bilinear forms on C^N with defining matrices A endowed with a quadratic Poisson structure of reflection equation type. The paper begins with a short description of previous studies of the structure, and then this structure is extended to systems of bilinear forms whose dynamics is governed by the natural action A\\mapsto B ABT} of the {GL}_N Poisson-Lie group on \\mathscr A. A classification is given of all possible quadratic brackets on (B, A)\\in {GL}_N× \\mathscr A preserving the Poisson property of the action, thus endowing \\mathscr A with the structure of a Poisson homogeneous space. Besides the product Poisson structure on {GL}_N× \\mathscr A, there are two other (mutually dual) structures, which (unlike the product Poisson structure) admit reductions by the Dirac procedure to a space of bilinear forms with block upper triangular defining matrices. Further generalisations of this construction are considered, to triples (B,C, A)\\in {GL}_N× {GL}_N× \\mathscr A with the Poisson action A\\mapsto B ACT}, and it is shown that \\mathscr A then acquires the structure of a Poisson symmetric space. Generalisations to chains of transformations and to the quantum and quantum affine algebras are investigated, as well as the relations between constructions of Poisson symmetric spaces and the Poisson groupoid. Bibliography: 30 titles.

Interacting composite fermions

DEFF Research Database (Denmark)

nrc762, nrc762

2016-01-01

Numerical studies by Wójs, Yi, and Quinn have suggested that an unconventional fractional quantum Hall effect is plausible at filling factors ν=1/3 and 1/5, provided the interparticle interaction has an unusual form for which the energy of two fermions in the relative angular momentum three channel...... as fractional quantum Hall effect of electrons at ν=4/11, 4/13, 5/13, and 5/17. I investigate in this article the nature of the fractional quantum Hall states at ν=4/5, 5/7, 6/17, and 6/7, which correspond to composite fermions at ν∗=4/3, 5/3, and 6/5, and find that all these fractional quantum Hall states...... are conventional. The underlying reason is that the interaction between composite fermions depends substantially on both the number and the direction of the vortices attached to the electrons. I also study in detail the states with different spin polarizations at 6/17 and 6/7 and predict the critical Zeeman...

Tensor completion and low-n-rank tensor recovery via convex optimization

International Nuclear Information System (INIS)

Gandy, Silvia; Yamada, Isao; Recht, Benjamin

2011-01-01

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers

Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Fermionic particles with positron-dependent mass in the presence of inversely quadratic Yukawa potential and tensor interaction

International Nuclear Information System (INIS)

Bahar, M.K.; Yasuk, F.

2013-01-01

Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)

Application of the bilinear compression function to calorimetry

CERN Document Server

Cattaneo, P W

2000-01-01

The energy dynamic range required by a calorimeter may exceed, if high speed is also required, the technical limitations of available ADCs. In this case the use of a dynamic compressor matching the energy range to the ADC range may be an adequate solution. The requirement for the compression function is to add an appropriately small quantization error to the calorimeter resolution. The bilinear compression function is easy to realize, it is therefore interesting to study the conditions under which it is adequate and which are the parameters of the compression curve, the slope ratio and the break point, minimizing the additional error due to quantization.

Application of the bilinear compression function to calorimetry

International Nuclear Information System (INIS)

Cattaneo, Paolo Walter

2000-01-01

The energy dynamic range required by a calorimeter may exceed, if high speed is also required, the technical limitations of available ADCs. In this case the use of a dynamic compressor matching the energy range to the ADC range may be an adequate solution. The requirement for the compression function is to add an appropriately small quantization error to the calorimeter resolution. The bilinear compression function is easy to realize, it is therefore interesting to study the conditions under which it is adequate and which are the parameters of the compression curve, the slope ratio and the break point, minimizing the additional error due to quantization

Fermion-number violation in regularizations that preserve fermion-number symmetry

Science.gov (United States)

Golterman, Maarten; Shamir, Yigal

2003-01-01

There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance (“fermion number”). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers gauge invariance to all orders in perturbation theory by including suitable counterterms. At the nonperturbative level, an apparent conflict then arises between the chiral U(1) symmetry of the regularized theory and the existence of ’t Hooft vertices in the renormalized theory. The only possible resolution of the paradox is that the chiral U(1) symmetry is broken spontaneously in the enlarged Hilbert space of the covariantly gauge-fixed theory. The corresponding Goldstone pole is unphysical. The theory must therefore be defined by introducing a small fermion-mass term that breaks explicitly the chiral U(1) invariance and is sent to zero after the infinite-volume limit has been taken. Using this careful definition (and a lattice regularization) for the calculation of correlation functions in the one-instanton sector, we show that the ’t Hooft vertices are recovered as expected.

Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions

International Nuclear Information System (INIS)

Dimopoulos, P.; Giusti, L.; Hernandez, P.; Palombi, F.; Pena, C.; Vladikas, A.; Wennekers, J.; Wittig, H.

2006-01-01

We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the ΔS=1 and ΔS=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays

Dynamical triangulated fermionic surfaces

International Nuclear Information System (INIS)

Ambjoern, J.; Varsted, S.

1990-12-01

We perform Monte Carlo simulations of randomly triangulated random surfaces which have fermionic world-sheet scalars θ i associated with each vertex i in addition to the usual bosonic world-sheet scalar χ i μ . The fermionic degrees of freedom force the internal metrics of the string to be less singular than the internal metric of the pure bosonic string. (orig.)

Tensor Transpose and Its Properties

OpenAIRE

Pan, Ran

2014-01-01

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.

Heavy fermion materials

International Nuclear Information System (INIS)

Smith, J.L.; Cooke, D.W.

1986-01-01

The heavy-fermion ground state occurs in a few select metallic compounds as a result of interactions between f-electron and conduction-electron spins. A characteristically large electronic heat capacity at low temperature indicates that the effective electron mass of these materials is more than two orders of magnitude greater than that expected for a free-electron metal. This heavy-fermion ground state can become superconducting or antiferromagnetic, exhibiting very unusual properties. These materials and the role of muon spin rotation in their study are briefly discussed

The bosonic mother of fermionic D-branes

OpenAIRE

Chattaraputi, Auttakit; Englert, Francois; Houart, Laurent; Taormina, Anne

2002-01-01

We extend the search for fermionic subspaces of the bosonic string compactified on E8 X SO(16) lattices to include all fermionic D-branes. This extension constraints the truncation procedure previously proposed and relates the fermionic strings, supersymmetric or not, to the global structure of the SO(16) group. The specific properties of all the fermionic D-branes are found to be encoded in its universal covering, whose maximal toroid defines the configuration space torus of their mother bos...

Liouville equation of relativistic charged fermion

International Nuclear Information System (INIS)

Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

1991-01-01

As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

Fermion systems in discrete space-time

International Nuclear Information System (INIS)

Finster, Felix

2007-01-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure

Fermion systems in discrete space-time

Energy Technology Data Exchange (ETDEWEB)

Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)

2007-05-15

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

Fermion Systems in Discrete Space-Time

OpenAIRE

Finster, Felix

2006-01-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

Fermion systems in discrete space-time

Science.gov (United States)

Finster, Felix

2007-05-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

Superfluid response in heavy fermion superconductors

Science.gov (United States)

Zhong, Yin; Zhang, Lan; Shao, Can; Luo, Hong-Gang

2017-10-01

Motivated by a recent London penetration depth measurement [H. Kim, et al., Phys. Rev. Lett. 114, 027003 (2015)] and novel composite pairing scenario [O. Erten, R. Flint, and P. Coleman, Phys. Rev. Lett. 114, 027002 (2015)] of the Yb-doped heavy fermion superconductor CeCoIn5, we revisit the issue of superfluid response in the microscopic heavy fermion lattice model. However, from the literature, an explicit expression for the superfluid response function in heavy fermion superconductors is rare. In this paper, we investigate the superfluid density response function in the celebrated Kondo-Heisenberg model. To be specific, we derive the corresponding formalism from an effective fermionic large- N mean-field pairing Hamiltonian whose pairing interaction is assumed to originate from the effective local antiferromagnetic exchange interaction. Interestingly, we find that the physically correct, temperature-dependent superfluid density formula can only be obtained if the external electromagnetic field is directly coupled to the heavy fermion quasi-particle rather than the bare conduction electron or local moment. Such a unique feature emphasizes the key role of the Kondo-screening-renormalized heavy quasi-particle for low-temperature/energy thermodynamics and transport behaviors. As an important application, the theoretical result is compared to an experimental measurement in heavy fermion superconductors CeCoIn5 and Yb-doped Ce1- x Yb x CoIn5 with fairly good agreement and the transition of the pairing symmetry in the latter material is explained as a simple doping effect. In addition, the requisite formalism for the commonly encountered nonmagnetic impurity and non-local electrodynamic effect are developed. Inspired by the success in explaining classic 115-series heavy fermion superconductors, we expect the present theory will be applied to understand other heavy fermion superconductors such as CeCu2Si2 and more generic multi-band superconductors.

Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

Directory of Open Access Journals (Sweden)

M. de la Sen

2008-01-01

Full Text Available This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.

Super boson-fermion correspondence

International Nuclear Information System (INIS)

Kac, V.G.; Leur van de, J.W.

1987-01-01

Since the pioneering work of Skyrme, the boson-fermion correspondence has been playing an increasingly important role in 2-dimensional quantum field theory. More recently, it has become an important ingredient in the work of the Kyoto school on the KP hierarchy of soliton equations. In the present paper we establish a super boson-fermion correspondence, having in mind its applications to super KP hierarchies

Fermion-scalar conformal blocks

Energy Technology Data Exchange (ETDEWEB)

Iliesiu, Luca [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States); Kos, Filip [Department of Physics, Yale University,217 Prospect Street, New Haven, CT 06520 (United States); Poland, David [Department of Physics, Yale University,217 Prospect Street, New Haven, CT 06520 (United States); School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr, Princeton, New Jersey 08540 (United States); Pufu, Silviu S. [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States); Simmons-Duffin, David [School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr, Princeton, New Jersey 08540 (United States); Yacoby, Ran [Joseph Henry Laboratories, Princeton University,Washington Road, Princeton, NJ 08544 (United States)

2016-04-13

We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.

Lattice degeneracies of geometric fermions

International Nuclear Information System (INIS)

Raszillier, H.

1983-05-01

We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)

ISAR Imaging of Ship Targets Based on an Integrated Cubic Phase Bilinear Autocorrelation Function

Directory of Open Access Journals (Sweden)

Jibin Zheng

2017-03-01

Full Text Available For inverse synthetic aperture radar (ISAR imaging of a ship target moving with ocean waves, the image constructed with the standard range-Doppler (RD technique is blurred and the range-instantaneous-Doppler (RID technique has to be used to improve the image quality. In this paper, azimuth echoes in a range cell of the ship target are modeled as noisy multicomponent cubic phase signals (CPSs after the motion compensation and a RID ISAR imaging algorithm is proposed based on the integrated cubic phase bilinear autocorrelation function (ICPBAF. The ICPBAF is bilinear and based on the two-dimensionally coherent energy accumulation. Compared to five other estimation algorithms, the ICPBAF can acquire higher cross term suppression and anti-noise performance with a reasonable computational cost. Through simulations and analyses with the synthetic model and real radar data, we verify the effectiveness of the ICPBAF and corresponding RID ISAR imaging algorithm.

Magnetic Majorana Fermions

Science.gov (United States)

Moessner, Roderich

Condensed matter systems provide emergent mini-universes in which quasiparticles may exist which do not correspond to any experimentally detected elementary particle. Topological quantum materials have been particularly productive in this regard, with the present search focussing on Majorana fermions, known theoretically already for decades. Here, we discuss manifestations of magnetic Majorana fermions in the Kitaev model. We place particular emphasis on their fate when perturbations, such as Heisenberg terms, are added to the ideal model system, and address experimental signatures of their vestiges in phases adjacent to the spin liquid.

Superconductivity in mixed boson-fermion systems

International Nuclear Information System (INIS)

Ioffe, L.; Larkin, A.I.; Ovchinnikov, Yu.N.; Yu, L.

1989-12-01

The superconductivity of mixed boson-fermion systems is studied using a simple boson-fermion transformation model. The critical temperature of the superconducting transition is calculated over a wide range of the narrow boson band position relative to the Fermi level. The BCS scenario and boson condensation picture are recovered in two limiting cases of high and low positions of boson band, respectively, with modifications due to boson-fermion interaction. (author). 11 refs

The tensor rank of tensor product of two three-qubit W states is eight

OpenAIRE

Chen, Lin; Friedland, Shmuel

2017-01-01

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.

Bilinear Inverse Problems: Theory, Algorithms, and Applications

Science.gov (United States)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical

Three mirror pairs of fermion families

International Nuclear Information System (INIS)

Montvay, I.

1988-01-01

A simple model with three mirror pairs of fermion families is considered which allows for a substantial mixing between the mirror fermion partners without conflicting with known phenomenology. (orig.)

Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

Science.gov (United States)

Blessy, B. S. Gnana; Latha, M. M.

2017-10-01

We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

Alternative to domain wall fermions

International Nuclear Information System (INIS)

Neuberger, H.

2002-01-01

An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain wall fermions will in general be associated with a condition number that is of the same order of magnitude as the product of the condition number of the linear problem in the physical dimensions by the inverse bare quark mass. Thus, the computational cost of implementing true domain wall fermions using a single conjugate gradient algorithm is of the same order of magnitude as that of implementing the overlap Dirac operator directly using two nested conjugate gradient algorithms. At a cost of about a factor of two in operation count it is possible to make the memory usage of direct implementations of the overlap Dirac operator independent of the accuracy of the approximation to the sign function and of the same order as that of standard Wilson fermions

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

Science.gov (United States)

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Bowen-York tensors

International Nuclear Information System (INIS)

Beig, Robert; Krammer, Werner

2004-01-01

For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York

Two-dimensional confinement of heavy fermions

International Nuclear Information System (INIS)

Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito

2010-01-01

Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)

Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

Science.gov (United States)

Dvoeglazov, V. V.

Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.

Fermion tunneling from higher-dimensional black holes

International Nuclear Information System (INIS)

Lin Kai; Yang Shuzheng

2009-01-01

Via the semiclassical approximation method, we study the 1/2-spin fermion tunneling from a higher-dimensional black hole. In our work, the Dirac equations are transformed into a simple form, and then we simplify the fermion tunneling research to the study of the Hamilton-Jacobi equation in curved space-time. Finally, we get the fermion tunneling rates and the Hawking temperatures at the event horizon of higher-dimensional black holes. We study fermion tunneling of a higher-dimensional Schwarzschild black hole and a higher-dimensional spherically symmetric quintessence black hole. In fact, this method is also applicable to the study of fermion tunneling from four-dimensional or lower-dimensional black holes, and we will take the rainbow-Finsler black hole as an example in order to make the fact explicit.

arXiv Charged Fermions Below 100 GeV

CERN Document Server

Egana-Ugrinovic, Daniel; Ruderman, Joshua T.

2018-05-03

How light can a fermion be if it has unit electric charge? We revisit the lore that LEP robustly excludes charged fermions lighter than about 100 GeV. We review LEP chargino searches, and find them to exclude charged fermions lighter than 90 GeV, assuming a higgsino-like cross section. However, if the charged fermion couples to a new scalar, destructive interference among production channels can lower the LEP cross section by a factor of 3. In this case, we find that charged fermions as light as 75 GeV can evade LEP bounds, while remaining consistent with constraints from the LHC. As the LHC collects more data, charged fermions in the 75–100 GeV mass range serve as a target for future monojet and disappearing track searches.

Bilinear approach to Kuperschmidt super-KdV type equations

Science.gov (United States)

Babalic, Corina N.; Carstea, A. S.

2018-06-01

Hirota bilinear form and soliton solutions for the super-KdV (Korteweg–de Vries) equation of Kuperschmidt (Kuper–KdV) are given. It is shown that even though the collision of supersolitons is more complicated than in the case of the supersymmetric KdV equation of Manin–Radul, the asymptotic effect of the interaction is simpler. As a physical application it is shown that the well-known FPU problem, having a phonon-mediated interaction of some internal degrees of freedom expressed through Grassmann fields, transforms to the Kuper–KdV equation in a multiple-scale approach.

Propagator of the lattice domain wall fermion and the staggered fermion

International Nuclear Information System (INIS)

Furui, S.

2009-01-01

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16 3 x 32 x 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling a s,g1 (q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling a s,g1 (q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling a s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q 2 ) with c ∼ 2.8 GeV 2 on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling a s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling a s,g1 (q) in the infrared region increases monotonically as q → 0. Above 2 GeV, the quark-gluon coupling a s,g1 (q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at http://dx.doi.org/10.1007/s00601-009-0053-4. (author)

Dense Chern-Simons matter with fermions at large N

Energy Technology Data Exchange (ETDEWEB)

Geracie, Michael; Goykhman, Mikhail; Son, Dam T. [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics,The University of Chicago, 5620 S. Ellis Av., Chicago, IL, 60637 (United States)

2016-04-18

In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the ’t Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.

Dense Chern-Simons matter with fermions at large N

International Nuclear Information System (INIS)

Geracie, Michael; Goykhman, Mikhail; Son, Dam T.

2016-01-01

In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the ’t Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.

Dense Chern-Simons matter with fermions at large N

Science.gov (United States)

Geracie, Michael; Goykhman, Mikhail; Son, Dam T.

2016-04-01

In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the 't Hooft coupling λ approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ideal gas law. Instead, it can be interpreted as a weakly coupled quantum Bose gas.

Phenomenology of colour exotic fermions

International Nuclear Information System (INIS)

Luest, D.

1986-01-01

The authors discuss the phenomenological consequences of a dynamical scenario according to which the electroweak symmetry breaking and generation of fermion masses is due to fermions that transform under high colour representations. Particular emphasis is given to the predictions for rare processes and to the spectrum of high colour boundstates. (Auth.)

Fermions in nonrelativistic AdS/CFT correspondence

International Nuclear Information System (INIS)

Akhavan, Amin; Alishahiha, Mohsen; Davody, Ali; Vahedi, Ali

2009-01-01

We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schroedinger group isometry. Although the boundary of the geometries with Schroedinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in nonrelativistic CFTs, though a nontrivial regularization may be needed.

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

2016-07-01

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

Heavy fermion and actinide materials

International Nuclear Information System (INIS)

1993-01-01

During this period, 1/N expansions have been systematically applied to the calculation of the properties of highly correlated electron systems. These studies include examinations of (a) the class of materials known as heavy fermion semi-conductors, (b) the high energy spectra of heavy fermion systems, and (c) the doped oxide superconductors

Fermion fractionization and index theorem

International Nuclear Information System (INIS)

Hirayama, Minoru; Torii, Tatsuo

1982-01-01

The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)

Composite fermions in the quantum Hall effect

International Nuclear Information System (INIS)

Johnson, B.L.; Kirczenow, G.

1997-01-01

The quantum Hall effect and associated quantum transport phenomena in low-dimensional systems have been the focus of much attention for more than a decade. Recent theoretical development of interesting quasiparticles - 'composite fermions' - has led to significant advances in understanding and predicting the behaviour of two-dimensional electron systems under high transverse magnetic fields. Composite fermions may be viewed as fermions carrying attached (fictitious) magnetic flux. Here we review models of the integer and fractional quantum Hall effects, including the development of a unified picture of the integer and fractional effects based upon composite fermions. The composite fermion picture predicts remarkable new physics: the formation of a Fermi surface at high magnetic fields, and anomalous ballistic transport, thermopower, and surface acoustic wave behaviour. The specific theoretical predictions of the model, as well as the body of experimental evidence for these phenomena are reviewed. We also review recent edge-state models for magnetotransport in low-dimensional devices based on the composite fermion picture. These models explain the fractional quantum Hall effect and transport phenomena in nanoscale devices in a unified framework that also includes edge state models of the integer quantum Hall effect. The features of the composite fermion edge-state model are compared and contrasted with those of other recent edge-state models of the fractional quantum Hall effect. (author)

Noether symmetry for non-minimally coupled fermion fields

International Nuclear Information System (INIS)

Souza, Rudinei C de; Kremer, Gilberto M

2008-01-01

A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period, behaving as a standard matter field

Finite boson mappings of fermion systems

International Nuclear Information System (INIS)

Johnson, C.W.; Ginocchio, J.N.

1994-01-01

We discuss a general mapping of fermion pairs to bosons that preserves Hermitian conjugation, with an eye towards producing finite and usable boson Hamiltonians that approximate well the low-energy dynamics of a fermion Hamiltonian

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

International Nuclear Information System (INIS)

Belvedere, L.V.; Souza Dutra, A. de; Natividade, C.P.; Queiroz, A.F. de

2002-01-01

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED 2 with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED 2 with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content

Current density tensors

Science.gov (United States)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Nonequilibrium fermion production in quantum field theory

International Nuclear Information System (INIS)

Pruschke, Jens

2010-01-01

The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio

Nonequilibrium fermion production in quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Pruschke, Jens

2010-06-16

The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio

Adaptive Energy-based Bilinear Control of First-Order 1-D Hyperbolic PDEs: Application to a One-Loop Parabolic Solar Collector Trough

KAUST Repository

Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem

2017-01-01

In this paper, the adaptive bilinear control of a first-order 1-D hyperbolic partial differential equation (PDE) with an unknown time-varying source term is investigated where only boundary measurements are available. By means of boundary injection, the bilinear adaptive law is developed in the Lyapunov approach. It consists of a state observer and an input adaptation law combined with a bilinear control method derived using an energy-like principle. Both global asymptotic practical convergence of the tracking error and input-to-state stability of the system are guaranteed. A potential application of this control strategy is the one-loop solar collector parabolic trough where the solar irradiance is the unknown input (source term) and the flow rate is the control variable. The objective is to drive the boundary temperature at the outlet to track a desired profile. Simulation results are provided to illustrate the performance of the proposed method.

Adaptive Energy-based Bilinear Control of First-Order 1-D Hyperbolic PDEs: Application to a One-Loop Parabolic Solar Collector Trough

KAUST Repository

Mechhoud, Sarra

2017-12-14

In this paper, the adaptive bilinear control of a first-order 1-D hyperbolic partial differential equation (PDE) with an unknown time-varying source term is investigated where only boundary measurements are available. By means of boundary injection, the bilinear adaptive law is developed in the Lyapunov approach. It consists of a state observer and an input adaptation law combined with a bilinear control method derived using an energy-like principle. Both global asymptotic practical convergence of the tracking error and input-to-state stability of the system are guaranteed. A potential application of this control strategy is the one-loop solar collector parabolic trough where the solar irradiance is the unknown input (source term) and the flow rate is the control variable. The objective is to drive the boundary temperature at the outlet to track a desired profile. Simulation results are provided to illustrate the performance of the proposed method.

On the spinor representation

Energy Technology Data Exchange (ETDEWEB)

Hoff da Silva, J.M.; Rogerio, R.J.B. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Villalobos, C.H.C. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)

2017-07-15

A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein-Dirac system that provides the spacetime generated by a fermion. (orig.)

Lattice fermions

Energy Technology Data Exchange (ETDEWEB)

Randjbar-Daemi, S

1995-12-01

The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if {Gamma}/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs.

Lattice fermions

International Nuclear Information System (INIS)

Randjbar-Daemi, S.

1995-12-01

The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs

Effect of CP violation in bilinear R-parity violation on baryogenesis

Energy Technology Data Exchange (ETDEWEB)

Cheriguene, Asma; Langenfeld, Ulrich; Porod, Werner [Universitaet Wuerzburg (Germany); Liebler, Stefan [Universitaet Wuppertal (Germany)

2013-07-01

Supersymmetric models where R-parity is broken via lepton number violation provides an intrinsically supersymmetric explanation for the observed neutrino. The complex phases of the corresponding parameters are constrained by the observed matter anti-matter asymmetry of the universe. Taking bilinear R-parity violation as framework in combination with the assumption of a large lepton asymmetry generated via the Affleck-Dine mechanism at the end of inflation we investigate these constraints in the parameter range compatible with neutrino data.

Interacting fermions on a random lattice

International Nuclear Information System (INIS)

Perantonis, S.J.; Wheater, J.F.

1988-01-01

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and tehy decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and taht the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings. (orig.)

Higgs inflation, seesaw physics and fermion dark matter

Directory of Open Access Journals (Sweden)

Nobuchika Okada

2015-07-01

Full Text Available We present an inflationary model in which the Standard Model Higgs doublet field with non-minimal coupling to gravity drives inflation, and the effective Higgs potential is stabilized by new physics which includes a dark matter particle and right-handed neutrinos for the seesaw mechanism. All of the new particles are fermions, so that the Higgs doublet is the unique inflaton candidate. With central values for the masses of the top quark and the Higgs boson, the renormalization group improved Higgs potential is employed to yield the scalar spectral index ns≃0.968, the tensor-to-scalar ratio r≃0.003, and the running of the spectral index α=dns/dln⁡k≃−5.2×10−4 for the number of e-folds N0=60 (ns≃0.962, r≃0.004, and α≃−7.5×10−4 for N0=50. The fairly low value of r≃0.003 predicted in this class of models means that the ongoing space and land based experiments are not expected to observe gravity waves generated during inflation.

Lattice quantum chromodynamics with approximately chiral fermions

International Nuclear Information System (INIS)

Hierl, Dieter

2008-05-01

In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

Lattice quantum chromodynamics with approximately chiral fermions

Energy Technology Data Exchange (ETDEWEB)

Hierl, Dieter

2008-05-15

In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

Grassmann phase space theory for fermions

Energy Technology Data Exchange (ETDEWEB)

Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)

2017-06-15

A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Transport properties of chiral fermions

Energy Technology Data Exchange (ETDEWEB)

Puhr, Matthias

2017-04-26

Anomalous transport phenomena have their origin in the chiral anomaly, the anomalous non-conservation of the axial charge, and can arise in systems with chiral fermions. The anomalous transport properties of free fermions are well understood, but little is known about possible corrections to the anomalous transport coefficients that can occur if the fermions are strongly interacting. The main goal of this thesis is to study anomalous transport effects in media with strongly interacting fermions. In particular, we investigate the Chiral Magnetic Effect (CME) in a Weyl Semimetal (WSM) and the Chiral Separation Effect (CSE) in finite-density Quantum Chromodynamics (QCD). The recently discovered WSMs are solid state crystals with low-energy excitations that behave like Weyl fermions. The inter-electron interaction in WSMs is typically very strong and non-perturbative calculations are needed to connect theory and experiment. To realistically model an interacting, parity-breaking WSM we use a tight-binding lattice Hamiltonian with Wilson-Dirac fermions. This model features a non-trivial phase diagram and has a phase (Aoki phase/axionic insulator phase) with spontaneously broken CP symmetry, corresponding to the phase with spontaneously broken chiral symmetry for interacting continuum Dirac fermions. We use a mean-field ansatz to study the CME in spatially modulated magnetic fields and find that it vanishes in the Aoki phase. Moreover, our calculations show that outside of the Aoki phase the electron interaction has only a minor influence on the CME. We observe no enhancement of the magnitude of the CME current. For our non-perturbative study of the CSE in QCD we use the framework of lattice QCD with overlap fermions. We work in the quenched approximation to avoid the sign problem that comes with introducing a finite chemical potential on the lattice. The overlap operator calls for the evaluation of the sign function of a matrix with a dimension proportional to the volume

Fermions

Directory of Open Access Journals (Sweden)

Boyle Peter

2018-01-01

Full Text Available We present results for the QED and strong isospin breaking corrections to the hadronic vacuum polarization using Nf = 2 + 1 Domain Wall fermions. QED is included in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. Results and statistical errors from both methods are directly compared with each other.

Squeezed fermions and back-to-back correlations

International Nuclear Information System (INIS)

Panda, P.K.; Krein, G.; Padula, S.S.; Csoergoe, T.; Hama, Y.

2001-01-01

Back-to-back correlations of asymptotic fermion pairs appear if in-medium interactions lead to mass modifications of fermion states in a thermalized medium. The back-to-back correlations of protons and anti-protons will be experimentally observable in ultrarelativistic heavy ion collisions. The strength of back-to-back correlations of fermions can be unlimitedly large, diverging as the momentum of the pair increases and the net baryon density decreases. (author)

Squeezed fermions and back-to-back correlations

Energy Technology Data Exchange (ETDEWEB)

Panda, P.K.; Krein, G.; Padula, S.S. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Csoergoe, T. [Hungarian Academy of Sciences, Budapest (Hungary). Research Institute for Particle and Nuclear Physics (RMKI, KFKI); Hama, Y. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica

2001-07-01

Back-to-back correlations of asymptotic fermion pairs appear if in-medium interactions lead to mass modifications of fermion states in a thermalized medium. The back-to-back correlations of protons and anti-protons will be experimentally observable in ultrarelativistic heavy ion collisions. The strength of back-to-back correlations of fermions can be unlimitedly large, diverging as the momentum of the pair increases and the net baryon density decreases. (author)

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

2017-01-01

We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...

Quasi-relativistic fermions and dynamical flavour oscillations

CERN Document Server

Alexandre, Jean; Mavromatos, Nick E.

2014-01-01

We introduce new Lorentz-symmetry violating kinematics for a four-fermion interaction model, where dynamical mass generation is allowed, irrespectively of the strength of the coupling. In addition, these kinematics lead to a quasi-relativistic dispersion relation, in the sense that it is relativistic in both the infrared and the ultraviolet, but not in an intermediate regime, characterized by the mass $M$. For two fermions, we show that a flavour-mixing mass matrix is generated dynamically, and the Lorentz symmetric limit $M\\to\\infty$ leads to two free relativistic fermions, with flavour oscillations. This model, valid for either Dirac or Majorana fermions, can describe any set of phenomenological values for the eigen masses and the mixing angle.

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

Wilson Fermions and Axion Electrodynamics in Optical Lattices

International Nuclear Information System (INIS)

Bermudez, A.; Martin-Delgado, M. A.; Mazza, L.; Rizzi, M.; Goldman, N.; Lewenstein, M.

2010-01-01

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.

Quantum geometry of the Dirac fermions

International Nuclear Information System (INIS)

Korchemskij, G.P.

1989-01-01

The bosonic path integral formalism is developed for Dirac fermions interacting with a nonabelian gauge field in the D-dimensional Euclidean space-time. The representation for the effective action and correlation functions of interacting fermions as sums over all bosonic paths on the complex projective space CP 2d-1 , (2d=2 [ D 2] is derived where all the spinor structure is absorbed by the one-dimensional Wess-Zumino term. It is the Wess-Zumino term that ensures all necessary properties of Dirac fermions under quantization. i.e., quantized values of the spin, Dirac equation, Fermi statistics. 19 refs

Fermionic NNLO contributions to Bhabha scattering

International Nuclear Information System (INIS)

Actis, S.; Riemann, T.; Czakon, M.; Uniwersytet Slaski, Katowice; Gluza, J.

2007-10-01

We derive the two-loop corrections to Bhabha scattering from heavy fermions using dispersion relations. The double-box contributions are expressed by three kernel functions. Convoluting the perturbative kernels with fermionic threshold functions or with hadronic data allows to determine numerical results for small electron mass m e , combined with arbitrary values of the fermion mass m f in the loop, m 2 e 2 f , or with hadronic insertions. We present numerical results for m f =m μ , m τ ,m top at typical small- and large-angle kinematics ranging from 1 GeV to 500 GeV. (orig.)

Experimental Study of Bilinear Initiating System Based on Hard Rock Pile Blasting

Directory of Open Access Journals (Sweden)

Yusong Miao

2017-01-01

Full Text Available It is difficult to use industrial explosives to excavate hard rock and achieve suitable blasting effect due to the low energy utilization rate resulting in large rocks and short blasting footage. Thus, improving the utilization ratio of the explosive energy is important. In this study, a novel bilinear initiation system based on hard rock blasting was proposed to improve the blasting effects. Furthermore, on the basis of the detonation wave collision theory, frontal collision, oblique reflection, and Mach reflection during detonation wave propagation were studied. The results show that the maximum detonation pressure at the Mach reflection point where the incident angle is 46.9° is three times larger than the value of the explosive complete detonation. Then, in order to analyze the crack propagation in different initiation forms, a rock fracture test slot was designed, and the results show that bilinear initiating system can change the energy distribution of explosives. Finally, field experiment was implemented at the hard rock pile blasting engineering, and experimental results show that the present system possesses high explosive energy utilization ratio and low rock fragments size. The results of this study can be used to improve the efficiency in hard rock blasting.

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

Fermions in Brans-Dicke cosmology

International Nuclear Information System (INIS)

Samojeden, L. L.; Devecchi, F. P.; Kremer, G. M.

2010-01-01

Using the Brans-Dicke theory of gravitation we put under investigation a hypothetical universe filled with a fermionic field (with a self-interaction potential) and a matter constituent ruled by a barotropic equation of state. It is shown that the fermionic field [in combination with the Brans-Dicke scalar field φ(t)] could be responsible for a final accelerated era, after an initial matter dominated period.

Generalized spin-wave theory: Application to the bilinear-biquadratic model

Science.gov (United States)

Muniz, Rodrigo A.; Kato, Yasuyuki; Batista, Cristian D.

2014-08-01

We present a mathematical framework for the multi-boson approach that has been used several times for treating spin systems. We demonstrate that the multi-boson approach corresponds to a generalization of the traditional spin-wave theory from SU(2) to SU(N), where N is the number of states of the local degree of freedom. Low-energy excitations are waves of the local order parameter that fluctuates in the SU(N) space of unitary transformations of the local spin states, instead of the SU(2) space of local spin rotations. Since the generators of the SU(N) group can be represented as bilinear forms in N-flavored bosons, the low-energy modes of the generalized spin-wave theory (GSWT) are described with N-1 different bosons, which provide a more accurate description of low-energy excitations even for the usual ferromagnetic and antiferromagnetic phases. The generalization enables the treatment of quantum spin systems whose ground states exhibit multipolar ordering as well as the detection of instabilities of magnetically ordered states (dipolar ordering) towards higher multipolar orderings. We illustrate the advantages of the GSWT by applying it to a bilinear-biquadratic model of arbitrary spin S on hypercubic lattices, and then analyzing the spectrum of dipolar phases in order to find their instabilities. In contrast to the known results for S=1 when the biquadratic term in the Hamiltonian is negative, we find that there is no nematic phase between the ferromagnetic or antiferromagnetic orderings for S>1.

The principle of the Fermionic projector

CERN Document Server

Finster, Felix

2006-01-01

The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionic projector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective...

Extra Z neutral bosons, families and heavy fermions

International Nuclear Information System (INIS)

Li Tiezhong

1989-08-01

The minimal Grand Unified Theories with three-family should include two extra Z neufral bosons which belong to the different broken scales. Georgi's argument on heavy Dirac fermions has been realized. These fermions should not be bizarre. The extra Z and Dirac fermions are not too heavy. The difficulty of the proton decay may be resolved

The hidden fermions in Z(2) theories

International Nuclear Information System (INIS)

Srednicki, M.

1983-01-01

Low dimensional Z(2) gauge theories have been rewritten in terms of locally coupled fermionic degrees of freedom by means of the Jordan-Wigner transformation. In this paper it is shown that higher dimensional Z(2) gauge theories are also fermionic theories in disguise. The SML solution to the 1+1 dimension Ising model is reviewed. Psi operators are represented pictorially as arrows, psi 1 points to the left, psi 2 to the right, each site of H a multiple of two operators. The 2+1 dimension Ising model is then considered. A fermion plaquette operator is introduced as the generator of a gauge symmetry for the fermionic H. Findings in 1+1 and 2+1 are then applied to 3+1 dimensional Z(2) gauge theory. A construction of this lattice is undertaken. Psi formalism replaces sigma formalism, as it permits extremely simple duality transformations to be made on any Z(2) Hamiltonian. It is shown that the fermionic formalism will lead to new ideas in Z(2) theories

On ghost fermions

International Nuclear Information System (INIS)

Grensing, G.

2002-01-01

The path integral for ghost fermions, which is heuristically made use of in the Batalin-Fradkin-Vilkovisky approach to quantization of constrained systems, is derived from first principles. The derivation turns out to be rather different from that of physical fermions since the definition of Dirac states for ghost fermions is subtle. With these results at hand, it is then shown that the nonminimal extension of the Becchi-Rouet-Stora-Tyutin operator must be chosen differently from the notorious choice made in the literature in order to avoid the boundary terms that have always plagued earlier treatments. Furthermore it is pointed out that the elimination of states with nonzero ghost number requires the introduction of a thermodynamic potential for ghosts; the reason is that Schwarz's Lefschetz formula for the partition function of the time-evolution operator is not capable, despite claims to the contrary, to get rid of nonzero ghost number states on its own. Finally, we comment on the problems of global topological nature that one faces in the attempt to obtain the solutions of the Dirac condition for physical states in a configuration space of nontrivial geometry; such complications give rise to anomalies that do not obey the Wess-Zumino consistency conditions. (orig.)

S-wave scattering of fermion revisited

International Nuclear Information System (INIS)

Rahaman, Anisur

2011-01-01

A model where a Dirac fermion is coupled to background dilaton field is considered to study s-wave scattering of fermion by a back ground dilaton black hole. It is found that an uncomfortable situation towards information loss scenario arises when one loop correction gets involved during bosonization.

Spectral intensity distribution of trapped fermions

Indian Academy of Sciences (India)

Trapped fermions; local density approximation; spectral intensity distribution function. ... Thus, cold atomic systems allow us to study interesting ... In fermions, synthetic non-Abelian gauge ... energy eigenstates of the isotropic harmonic oscillator [26–28]. ... d i=1. (ni + 1. 2. )ω0. In calculating the SIDF exactly these eigenfunc-.

Robust fuzzy output feedback controller for affine nonlinear systems via T-S fuzzy bilinear model: CSTR benchmark.

Science.gov (United States)

Hamdy, M; Hamdan, I

2015-07-01

In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

FCNC Effects in a Minimal Theory of Fermion Masses

CERN Document Server

Buras, Andrzej J; Pokorski, Stefan; Ziegler, Robert

2011-01-01

As a minimal theory of fermion masses we extend the SM by heavy vectorlike fermions, with flavor-anarchical Yukawa couplings, that mix with chiral fermions such that small SM Yukawa couplings arise from small mixing angles. This model can be regarded as an effective description of the fermionic sector of a large class of existing flavor models and thus might serve as a useful reference frame for a further understanding of flavor hierarchies in the SM. Already such a minimal framework gives rise to FCNC effects through exchange of massive SM bosons whose couplings to the light fermions get modified by the mixing. We derive general formulae for these corrections and discuss the bounds on the heavy fermion masses. Particularly stringent bounds, in a few TeV range, come from the corrections to the Z couplings.

Trapped Fermions with Density Imbalance in the Bose-Einstein Condensate Limit

International Nuclear Information System (INIS)

Pieri, P.; Strinati, G.C.

2006-01-01

We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms

On the trace anomaly of a Weyl fermion

Energy Technology Data Exchange (ETDEWEB)

Bastianelli, Fiorenzo; Martelli, Riccardo [Dipartimento di Fisica e Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy)

2016-11-29

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa’s method supplemented by a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.

Phases of renormalized lattice gauge theories with fermions

International Nuclear Information System (INIS)

Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)

1979-01-01

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory

On the regularized fermionic projector of the vacuum

Science.gov (United States)

Finster, Felix

2008-03-01

We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional MP-product. The method is to analyze regularization tails with a power law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multilayer structure of the fermionic projector near the light cone. Furthermore, we construct regularizations which go beyond the distributional MP-product in that they yield additional distributional contributions supported at the origin. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.

On the regularized fermionic projector of the vacuum

International Nuclear Information System (INIS)

Finster, Felix

2008-01-01

We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional MP-product. The method is to analyze regularization tails with a power law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multilayer structure of the fermionic projector near the light cone. Furthermore, we construct regularizations which go beyond the distributional MP-product in that they yield additional distributional contributions supported at the origin. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed

Relations between bilinear multipliers on Rn,Tn Rn,Tn Rn,Tn and Zn

Indian Academy of Sciences (India)

Since then the study of bilinear multiplier operators which commute with simultaneous translations have attracted a great deal of ... Unlike in the linear case, the boundedness of the symbol ψC is not known. In this article we will be dealing with .... For the converse, let ψ ∈ M p3 p1,p2 (Z). For f, g ∈ C∞ c (R), we have.

Gogny interactions with tensor terms

Energy Technology Data Exchange (ETDEWEB)

Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)

2016-07-15

We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)

Perturbative improvement of staggered fermions using fat links

International Nuclear Information System (INIS)

Lee, Weonjong

2002-01-01

We study the possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple SU(3) projections, uniqueness, and equivalence. As a result of these theorems, we show that, at the one-loop level, the renormalization of staggered fermion operators is identical between SU(3) projected Fat7 links and hypercubic links, as long as the action and operators are constructed by imposing the same perturbative improvement condition. In addition, we propose a new view of SU(3) projection as a tool of tadpole improvement for the staggered fermion doublers. As a conclusion, we present alternative choices of constructing fat links to improve the staggered fermion action and operators, which deserve further investigation

Level Density In Interacting Boson-Fermion-Fermion Model (IBFFM) Of The Odd-Odd Nucleus 196Au

International Nuclear Information System (INIS)

Kabashi, Skender; Bekteshi, Sadik

2007-01-01

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

Tensor structure for Nori motives

OpenAIRE

Barbieri-Viale, Luca; Huber, Annette; Prest, Mike

2018-01-01

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.

Cholesky-like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms

Czech Academy of Sciences Publication Activity Database

Rozložník, Miroslav; Okulicka-Dłużewska, F.; Smoktunowicz, A.

2015-01-01

Roč. 36, č. 2 (2015), s. 727-751 ISSN 0895-4798 R&D Projects: GA ČR(CZ) GAP108/11/0853 Institutional support: RVO:67985807 Keywords : symmetric indefinite matrices * Cholesky-like factorization * orthogonalization techniques * indefinite bilinear forms * Gram-Schmidt process * rounding error analysis Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015

An exact fermion-pair to boson mapping

International Nuclear Information System (INIS)

Johnson, C.W.

1993-01-01

I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model

Collective Interference of Composite Two-Fermion Bosons

DEFF Research Database (Denmark)

Tichy, Malte; Bouvrie, Peter Alexander; Mølmer, Klaus

2012-01-01

The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us...... to provide the full Hong–Ou–Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson....

Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.

Science.gov (United States)

Iwasaki, Tohru; Furukawa, Tetsuo

2016-05-01

In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

Frequency interval balanced truncation of discrete-time bilinear systems

DEFF Research Database (Denmark)

Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza

2016-01-01

This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals...... are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new...... generalized frequency interval controllability and observability gramians as part of the balanced truncation framework are provided to demonstrate the performance of the proposed method....

Zero-energy modes, charge conjugation, and fermion number

International Nuclear Information System (INIS)

Sudarshan, E.C.G.; Yajnik, U.A.

1986-01-01

States with a half-integer fermion number occur when a fermionic field coupled to a soliton possesses a zero mode. This paper spells out the circumstances under which one can retain an integer fermion number as also a charge-conjugation-invariant ground state. It is necessary to make the representation reducible but it is kept irreducible by introducing an additional operator

Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

OpenAIRE

Loveridge, Lee C.

2004-01-01

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

Science.gov (United States)

Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

Unifying neural-network quantum states and correlator product states via tensor networks

Science.gov (United States)

Clark, Stephen R.

2018-04-01

Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose (unnormalised) amplitudes in a fixed basis can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer (2017 Science 355 602) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators making them uniquely unbiased geometrically. The appearance of GHZ correlators also relates NQS to canonical polyadic decompositions of tensors. Another immediate implication of the NQS equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superpositions of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.

Development of the Tensoral Computer Language

Science.gov (United States)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

Science.gov (United States)

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Killing-Yano tensors and Nambu mechanics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3

Fermion families and vacuum in the two measures theory

International Nuclear Information System (INIS)

Guendelman, E.; Kaganovich, A.

2005-01-01

We present an alternative gravity and matter fields theory where the consistency condition of equations of motion yields strong correlation between states of 'primordial' fermion fields and local value of the scalar fields (dilaton and Higgs) energy density. The same 'primordial' fermion field at different densities can be either in states of regular fermionic matter or in states presumably corresponding to the dark fermionic matter. In regime of the fermion densities typical for normal particle physics, each of the primordial fermions splits into three generations identified with regular fermions. When restricting ourselves to the first two fermion generations, the theory reproduces general relativity and regular particle theory. As fermion energy density is comparable with vacuum energy density, the theory allows new type of states. Such Cosmo-Low Energy Physics (CLEP) state is studied in the framework of the model where FRW universe filled with homogeneous scalar field and uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are drawn into cosmological expansion by means of dynamically changing their own parameters. Some of the features of the CLEP state in the late time universe: neutrino mass increases as α 3/2 (α = α(t) is the scale factor); its energy density scales as a sort of dark energy and approaches constant as α→∞; this cold dark matter possesses negative pressure and its equation of state approaches that of the cosmological constant as α→∞; the total energy density of such universe is less than it would be in the universe free of fermionic matter at all. The latter means that nonrelativistic neutrinos are able to produce expanding bubbles of the CLEP state playing the role of a true 'cosmological vacuum' surrounded by a 'regular' vacuum. (authors)

Born-Kothari Condensation for Fermions

Directory of Open Access Journals (Sweden)

Arnab Ghosh

2017-09-01

Full Text Available In the spirit of Bose–Einstein condensation, we present a detailed account of the statistical description of the condensation phenomena for a Fermi–Dirac gas following the works of Born and Kothari. For bosons, while the condensed phase below a certain critical temperature, permits macroscopic occupation at the lowest energy single particle state, for fermions, due to Pauli exclusion principle, the condensed phase occurs only in the form of a single occupancy dense modes at the highest energy state. In spite of these rudimentary differences, our recent findings [Ghosh and Ray, 2017] identify the foregoing phenomenon as condensation-like coherence among fermions in an analogous way to Bose–Einstein condensate which is collectively described by a coherent matter wave. To reach the above conclusion, we employ the close relationship between the statistical methods of bosonic and fermionic fields pioneered by Cahill and Glauber. In addition to our previous results, we described in this mini-review that the highest momentum (energy for individual fermions, prerequisite for the condensation process, can be specified in terms of the natural length and energy scales of the problem. The existence of such condensed phases, which are of obvious significance in the context of elementary particles, have also been scrutinized.

Chiral composite fermions without U(1)'s

International Nuclear Information System (INIS)

Nelson, A.E.

1986-01-01

Some models are discussed which seem likely to produce composite fermions with masses protected only by nonabelian global symmetries. A subgroup of the original global symmetries can be weakly gauged to produce small masses for the fermions. A new feature of these models is that the original global symmetries contain no abelian factors and below the confinement scale there are neither exactly massless fermions nor Goldstone bosons. A candidate is given for a potentially realistic model with up to six families of quarks and leptons. (orig.)

Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8

International Nuclear Information System (INIS)

1998-01-01

The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U A (1) symmetry and the η' for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk

Fermion structures of state vectors of the Schwinger model with multi-fermions

International Nuclear Information System (INIS)

Nakawaki, Yuji

1983-01-01

Coulomb-gauge Schwinger model with multi-fermions is formulated consistently in a box [-L, L] by introducing true dynamical degrees of freedom of electromagnetic fields, namely zero-mode part A 1 sup((0)) of A 1 and its canonical conjugate momentum π 1 sup((0)). State vectors are constructed of free massless fermion operators and zero-mode operators A 1 sup((0)) and π 1 sup((0)) and it is clarified how and why multifermion condensations become degenerate ground states and chiral invariance is spontaneously broken. It is also examined that physical space of covariant gauge Schwinger model is isomorphic to that of Coulomb-gauge Schwinger model. (author)

Four fermion interaction near four dimensions

International Nuclear Information System (INIS)

Zinn-Justin, J.

1991-01-01

It is known that field theories with attractive four-point fermion interactions can produce scalar bound states: Fermion mass generation by spontaneous chiral symmetry breaking associated with such fermion bound states provides an attractive mechanism for building models of composite Higgs bosons. The ratio of fermion and boson masses can then be predicted while it seems to be a free parameter in similar models where a boson field explicitly appears in the action. The main problem is that the corresponding models are renormalizable only in two dimensions, in contrast with models with explicit bosons. Many fermion models with four-point interaction are asymptotically free in two dimensions and then behave also like renormalizable models in higher dimensions, at least within the framework of some 1/N expansion. On the other hand mass ratio predictions also follow in the models with explicit bosons, when they have an IR fixed point, from the additional natural assumption that coupling constants have generic values at the cut-off scale. To the model with a four fermion interaction one can associate an effective model containing an additional scalar field, renormalizable in four dimensions, which has the same large distance, small momentum physics, at least to all orders in some 1/N expansion. Even the leading corrections corresponding to irrelevant or marginal operators are identical. This property is important in four dimensions where the IR fixed point coupling constants vanish: The correction amplitudes can be varied by changing the coupling constants in the renormalizable model and the cut-off function in the perturbatively non-renormalizable model. We shall consider here for definiteness only the Gross-Neveu model but it will be clear that the arguments are more general

Unconventional superconductivity in heavy-fermion compounds

Energy Technology Data Exchange (ETDEWEB)

White, B.D. [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Center for Advanced Nanoscience, University of California, San Diego, La Jolla, CA 92093 (United States); Thompson, J.D. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Maple, M.B., E-mail: mbmaple@ucsd.edu [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Center for Advanced Nanoscience, University of California, San Diego, La Jolla, CA 92093 (United States)

2015-07-15

Highlights: • Quasiparticles in heavy-fermion compounds are much heavier than free electrons. • Superconductivity involves pairing of these massive quasiparticles. • Quasiparticle pairing mediated by magnetic or quadrupolar fluctuations. • We review the properties of superconductivity in heavy-fermion compounds. - Abstract: Over the past 35 years, research on unconventional superconductivity in heavy-fermion systems has evolved from the surprising observations of unprecedented superconducting properties in compounds that convention dictated should not superconduct at all to performing explorations of rich phase spaces in which the delicate interplay between competing ground states appears to support emergent superconducting states. In this article, we review the current understanding of superconductivity in heavy-fermion compounds and identify a set of characteristics that is common to their unconventional superconducting states. These core properties are compared with those of other classes of unconventional superconductors such as the cuprates and iron-based superconductors. We conclude by speculating on the prospects for future research in this field and how new advances might contribute towards resolving the long-standing mystery of how unconventional superconductivity works.

Categorical Tensor Network States

Directory of Open Access Journals (Sweden)

Jacob D. Biamonte

2011-12-01

Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

The super W∞ algebra

International Nuclear Information System (INIS)

Bergshoeff, E.; Pope, C.N.; Sezgin, E.; Shen, X.; Romans, L.J.

1990-01-01

We construct a higher-spin N=2 superalgebra whose bosonic sector is W ∞ +W 1+∞ . It can be realised in terms of bilinear currents involving free complex bosonic and fermionic fields. We also discuss the spectral flow, and various truncations. (orig.)

Strongly-interacting mirror fermions at the LHC

Directory of Open Access Journals (Sweden)

Triantaphyllou George

2017-01-01

Full Text Available The introduction of mirror fermions corresponding to an interchange of leftwith right-handed fermion quantum numbers of the Standard Model can lead to a model according to which the BEH mechanism is just an effective manifestation of a more fundamental theory while the recently-discovered Higgs-like particle is composite. This is achieved by a non-abelian gauge symmetry encompassing three mirror-fermion families strongly coupled at energies near 1 TeV. The corresponding non-perturbative dynamics lead to dynamical mirror-fermion masses between 0.14 - 1.2 TeV. Furthermore, one expects the formation of composite states, i.e. “mirror mesons”, with masses between 0.1 and 3 TeV. The number and properties of the resulting new degrees of freedom lead to a rich and interesting phenomenology, part of which is analyzed in the present work.

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

Gauge invariant Barr-Zee type contributions to fermionic EDMs in the two-Higgs doublet models

International Nuclear Information System (INIS)

Abe, Tomohiro; Hisano, Junji; Kitahara, Teppei; Tobioka, Kohsaku

2014-01-01

We calculate all gauge invariant Barr-Zee type contributions to fermionic electric dipole moments (EDMs) in the two-Higgs doublet models (2HDM) with softly broken Z 2 symmetry. We start by studying the tensor structure of h→VV′ part in the Barr-Zee diagrams, and we calculate the effective couplings in a gauge invariant way by using the pinch technique. Then we calculate all Barr-Zee diagrams relevant for electron and neutron EDMs. We make bounds on the parameter space in type-I, type-II, type-X, and type-Y 2HDMs. The electron and neutron EDMs are complementary to each other in discrimination of the 2HDMs. Type-II and type-X 2HDMs are strongly constrained by recent ACME experiment’s result, and future experiments of electron and neutron EDMs may search O(10) TeV physics

Stochastic bosonization for a d ≥ 3 Fermi system

International Nuclear Information System (INIS)

Accardi, L.; Lu, Y.G.; Mastropietro, V.

1997-01-01

We consider a system of fermions interacting via an external field and we prove, in d ≥ 3, that a suitable collective operator, bilinear in the fermionic fields, in the stochastic limit becomes a boson quantum brownian motion. The evolution operator after the limit satisfies a quantum stochastic differential equation, in which the imaginary part of the Ito correction is the ground state shift while its real part is the lifetime of the ground state. (orig.)

Fermionic bound states in distinct kinklike backgrounds

Energy Technology Data Exchange (ETDEWEB)

Bazeia, D. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Mohammadi, A. [Universidade Federal de Campina Grande, Departamento de Fisica, Caixa Postal 10071, Campina Grande, Paraiba (Brazil)

2017-04-15

This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have a similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and we consider two distinct boson-fermion interactions, one motivated by supersymmetry and the other described by the standard Yukawa coupling. (orig.)

Baby Skyrme model and fermionic zero modes

Science.gov (United States)

Queiruga, J. M.

2016-09-01

In this work we investigate some features of the fermionic sector of the supersymmetric version of the baby Skyrme model. We find that, in the background of Bogomol'nyi-Prasad-Sommerfield compact baby Skyrmions, fermionic zero modes are confined to the defect core. Further, we show that, while three Supersymmetry (SUSY) generators are broken in the defect core, SUSY is completely restored outside. We study also the effect of a D-term deformation of the model. Such a deformation allows for the existence of fermionic zero modes and broken SUSY outside the compact defect.

Instantons and Massless Fermions in Two Dimensions

Science.gov (United States)

Callan, C. G. Jr.; Dashen, R.; Gross, D. J.

1977-05-01

The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.

Massive chiral fermions: a natural account of chiral phenomenology in the framework of Dirac's fermion theory

International Nuclear Information System (INIS)

Ziino, G.

1989-01-01

We assume a strictly invariant definition of the Dirac parity operator under fermion ↔ antifermion exchange. We see that the opposite-intrinsic-parity condition then requires two opposite-mass Dirac equations for the fermion and the antifermion. This leads us to introduce an asymptotically left-handed (fermion) and right-handed (antifermion) chiral field, as just an alternative basis in the internal space spanned by the new pair of charge-conjugate Dirac fields. Hence a dual intrinsic model of a spin - 1/2 massive fermion is drawn: it predicts the coexistence of two anticommuting general varieties of conserved charges, namely a scalar variety, responsible for parity-invariant phenomenology, plus a pseudoscalar one, responsible for chiral phenomenology. In this light, CP-symmetry is seen to be nothing but P-symmetry; and a spontaneous CP-violation mechanism is also derived, that should work in any single process occurring via both scalar-and pseudoscalar-charge interactions. We show, at last, that our scheme automatically yields Weyl's one for a merely left-handed neutrino and a merely right-handed antineutrino, further assigning them the special meaning of pure pseudoscalar-charge objects. Some general consequences as regards magnetic monopoles are briefly discussed too

Calculation of CWKB envelope in boson and fermion productions

International Nuclear Information System (INIS)

Biswas, S.; Chowdhury, I.

2007-01-01

We present the calculation of envelope of boson and of both low-and high-mass fermion production at the end of inflation when the coherently oscillating inflations decay into bosons and fermions. We consider three different models of inflation and use CWKB technique to calculate the envelope to understand the structure of resonance band formation. We observe that though low-mass fermion production is not effective in preheating because of Pauli blocking, it is quite probable for high-mass fermion to take part in pre heating. (author)

Spin-excited oscillations in two-component fermion condensates

International Nuclear Information System (INIS)

Maruyama, Tomoyuki; Bertsch, George F.

2006-01-01

We investigate collective spin excitations in two-component fermion condensates with special consideration of unequal populations of the two components. The frequencies of monopole and dipole modes are calculated using Thomas-Fermi theory and the scaling approximation. As the fermion-fermion coupling is varied, the system shows various phases of the spin configuration. We demonstrate that spin oscillations have more sensitivity to the spin phase structures than the density oscillations

The geomagnetic field gradient tensor

DEFF Research Database (Denmark)

Kotsiaros, Stavros; Olsen, Nils

2012-01-01

We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...

Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

Iterative methods for overlap and twisted mass fermions

International Nuclear Information System (INIS)

Chiarappa, T.; Jansen, K.; Shindler, A.; Wetzorke, I.; Scorzato, L.; Urbach, C.; Wenger, U.

2006-09-01

We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 MeV and 720 MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator. (orig.)

Iterative methods for overlap and twisted mass fermions

Energy Technology Data Exchange (ETDEWEB)

Chiarappa, T. [Univ. di Milano Bicocca (Italy); Jansen, K.; Shindler, A.; Wetzorke, I. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Nagai, K.I. [Wuppertal Univ. (Gesamthochschule) (Germany). Fachbereich Physik; Papinutto, M. [INFN Sezione di Roma Tre, Rome (Italy); Scorzato, L. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy); Urbach, C. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Wenger, U. [ETH Zuerich (Switzerland). Inst. fuer Theoretische Physik

2006-09-15

We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230 MeV and 720 MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator. (orig.)

Symmetric Tensor Decomposition

DEFF Research Database (Denmark)

Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

2010-01-01

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....

Second order statistics of bilinear forms of robust scatter estimators

KAUST Repository

Kammoun, Abla

2015-08-12

This paper lies in the lineage of recent works studying the asymptotic behaviour of robust-scatter estimators in the case where the number of observations and the dimension of the population covariance matrix grow at infinity with the same pace. In particular, we analyze the fluctuations of bilinear forms of the robust shrinkage estimator of covariance matrix. We show that this result can be leveraged in order to improve the design of robust detection methods. As an example, we provide an improved generalized likelihood ratio based detector which combines robustness to impulsive observations and optimality across the shrinkage parameter, the optimality being considered for the false alarm regulation.

Chiral fermions in asymptotically safe quantum gravity.

Science.gov (United States)

Meibohm, J; Pawlowski, J M

2016-01-01

We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.

Observation of three-component fermions in the topological semimetal molybdenum phosphide

Science.gov (United States)

Lv, B. Q.; Feng, Z.-L.; Xu, Q.-N.; Gao, X.; Ma, J.-Z.; Kong, L.-Y.; Richard, P.; Huang, Y.-B.; Strocov, V. N.; Fang, C.; Weng, H.-M.; Shi, Y.-G.; Qian, T.; Ding, H.

2017-06-01

In quantum field theory, Lorentz invariance leads to three types of fermion—Dirac, Weyl and Majorana. Although the existence of Weyl and Majorana fermions as elementary particles in high-energy physics is debated, all three types of fermion have been proposed to exist as low-energy, long-wavelength quasiparticle excitations in condensed-matter systems. The existence of Dirac and Weyl fermions in condensed-matter systems has been confirmed experimentally, and that of Majorana fermions is supported by various experiments. However, in condensed-matter systems, fermions in crystals are constrained by the symmetries of the 230 crystal space groups rather than by Lorentz invariance, giving rise to the possibility of finding other types of fermionic excitation that have no counterparts in high-energy physics. Here we use angle-resolved photoemission spectroscopy to demonstrate the existence of a triply degenerate point in the electronic structure of crystalline molybdenum phosphide. Quasiparticle excitations near a triply degenerate point are three-component fermions, beyond the conventional Dirac-Weyl-Majorana classification, which attributes Dirac and Weyl fermions to four- and two-fold degenerate points, respectively. We also observe pairs of Weyl points in the bulk electronic structure of the crystal that coexist with the three-component fermions. This material thus represents a platform for studying the interplay between different types of fermions. Our experimental discovery opens up a way of exploring the new physics of unconventional fermions in condensed-matter systems.

Exotic fermions and electric dipole moments

International Nuclear Information System (INIS)

Joshipura, A.S.

1991-01-01

The contributions of mirror fermions to the electric dipole moments (EDM's) of leptons and neutrons are studied using the available limits on the mixing of the relevant fermions to their mirror partners. These limits imply EDM's several orders of magnitude larger than the current experimental bounds in the case of the electron and the neutron if the relevant CP-violating phases are not unnaturally small. If these phases are large, then the bounds on the EDM's can be used to improve upon the limits on mixing between the ordinary (f) and the mirror (F) fermions. In the specific case of the latter mixing angle being given by (m f /M F ) 1/2 , one can obtain the electron and the neutron EDM's close to experimental bounds

Fermionic constructions of exceptional Kac-Moody algebras

International Nuclear Information System (INIS)

Schwimmer, A.

1985-01-01

The author discusses the fermionic representations of SO(2n) Kac Moody algebras. He describes construction of the E/sub 8/ algebra in terms of free fermionic operators, and generalises procedures for the basic representations of the Kac-Moody algebras appearing in Freudenthal's magic square

Two-dimensional thermofield bosonization II: Massive fermions

International Nuclear Information System (INIS)

Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

2008-01-01

We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield formulation. Thereby we establish in thermofield dynamics the formal equivalence of the massive free fermion theory with the sine-Gordon thermofield model for a particular value of the sine-Gordon parameter. We extend the thermofield bosonization to include the massive Thirring model

Three-dimensional Majorana fermions in chiral superconductors.

Science.gov (United States)

Kozii, Vladyslav; Venderbos, Jörn W F; Fu, Liang

2016-12-01

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs 4 Sb 12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Monograph On Tensor Notations

Science.gov (United States)

Sirlin, Samuel W.

1993-01-01

Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

Axial anomalies of Lifshitz fermions

CERN Document Server

Bakas, Ioannis

2011-01-01

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the eta-invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non-relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Horava-Lifshitz theory and find that the index is non-zero provided that the space-time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2)xU(1) isom...

Exotic fermions in the left-right symmetric model

International Nuclear Information System (INIS)

Choi, J.; Volkas, R.R.

1992-01-01

A systematic study is made of non-standard fermion multiplets in left-right symmetric models with gauge group SU(3) x SU(2) L x SU(2) R x U(1) BL . Constraints from gauge anomaly cancellation and invariance of Yukawa coupling terms are used to define interesting classes of exotic fermions. The standard quark lepton spectrum of left-right symmetric models was identified as the simplest member of an infinite class. Phenomenological implications of the next simplest member of this class are then studied. Classes of exotic fermions which may couple to the standard fermions through doublet Higgs bosons were also considered, then shown that some of these exotics may be used to induce a generalised universal see-saw mechanism. 12 refs., 1 tab

Cartesian tensors an introduction

CERN Document Server

Temple, G

2004-01-01

This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t

Spin-dependent level density in interacting Boson-Fermion-Fermion model of the Odd-Odd Nucleus 196Au

International Nuclear Information System (INIS)

Kabashi, S.; Bekteshi, S.; Ahmetaj, S.; Shaqiri, Z.

2009-01-01

The level density of the odd-odd nucleus 196 Au 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)

Strong correlations in few-fermion systems

Energy Technology Data Exchange (ETDEWEB)

Bergschneider, Andrea

2017-07-26

In this thesis, I report on the deterministic preparation and the observation of strongly correlated few-fermion systems in single and double-well potentials. In a first experiment, we studied a system of one impurity interacting with a number of majority atoms which we prepared in a single potential well in the one-dimensional limit. With increasing number of majority particles, we observed a decrease in the quasi-particle residue which is in agreement with expectations from the Anderson orthogonality catastrophe. In a second experiment, we prepared two fermions in a double-well potential which represents the fundamental building block of the Fermi-Hubbard model. By increasing the repulsion between the two fermions, we observed the crossover into the antiferromagnetic Mott-insulator regime. Furthermore, I describe a new imaging technique, which allows spin-resolved single-atom detection both in in-situ and in time-of-flight. We use this technique to investigate the emergence of momentum correlations of two repulsive fermions in the ground state of the double well. With the methods developed in this thesis, we have established a framework for quantum simulation of strongly correlated many-body systems in tunable potentials.

Pole mass, width, and propagators of unstable fermions

International Nuclear Information System (INIS)

Kniehl, B.A.; Sirlin, A.

2008-01-01

The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. General expressions for the unrenormalized and renormalized dressed propagators of unstable fermions and their field-renormalization constants are presented. (orig.)

Coherent states in the fermionic Fock space

International Nuclear Information System (INIS)

Oeckl, Robert

2015-01-01

We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions. (paper)

Nambu-Jona-Lasinio model with Wilson fermions

DEFF Research Database (Denmark)

Rantaharju, Jarno; Drach, Vincent; Pica, Claudio

2017-01-01

We present a lattice study of a Nambu-Jona-Lasinio (NJL) model using Wilson fermions. Four-fermion interactions are a natural part of several extensions of the Standard Model, appearing as a low-energy description of a more fundamental theory. In models of dynamical electroweak symmetry breaking...

MATLAB tensor classes for fast algorithm prototyping.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

2004-10-01

Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

On Efficient Numerical Approximation of the Bilinear Form c* A(-1)b

Czech Academy of Sciences Publication Activity Database

Strakoš, Z.; Tichý, Petr

2011-01-01

Roč. 33, č. 2 (2011), s. 565-587 ISSN 1064-8275 R&D Projects: GA AV ČR IAA100300802 Grant - others:GA ČR(CZ) GA201/09/0917; GA AV ČR(CZ) M100300901 Program:GA Institutional research plan: CEZ:AV0Z10300504 Keywords : bilinear forms * scattering amplitude * method of moments * Krylov subspace methods * conjugate gradient method * biconjugate gradient method * Lanczos algorithm * Arnoldi algorithm * Gauss-Christoffel quadrature * model reduction Subject RIV: BA - General Mathematics Impact factor: 1.569, year: 2011

On the disordered fermion couplings

International Nuclear Information System (INIS)

Bernaschi, M.; Cabasino, S.; Marinari, E.; Rome-2 Univ.; Sarno, R.; Rome-1 Univ.

1989-01-01

We study the possibility of avoiding the fermion doubling problem by using a random coupling. We use numerical simulations in order to study the theory in the strong disorder region. We find a sharp crossover as a function of the strength of the disorder. For weak quenched disorder we find that the species doubling survives, while for strong quenched disorder only with a particular choice of the random term (antihermitian) it is possible to get a theory that seems to avoid fermion doubling. (orig.)

Fermions as generalized Ising models

Directory of Open Access Journals (Sweden)

C. Wetterich

2017-04-01

Full Text Available We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.

Turning Avatar into Realistic Human Expression Using Linear and Bilinear Interpolations

Science.gov (United States)

Hazim Alkawaz, Mohammed; Mohamad, Dzulkifli; Rehman, Amjad; Basori, Ahmad Hoirul

2014-06-01

The facial animation in term of 3D facial data has accurate research support of the laser scan and advance 3D tools for complex facial model production. However, the approach still lacks facial expression based on emotional condition. Though, facial skin colour is required to offers an effect of facial expression improvement, closely related to the human emotion. This paper presents innovative techniques for facial animation transformation using the facial skin colour based on linear interpolation and bilinear interpolation. The generated expressions are almost same to the genuine human expression and also enhance the facial expression of the virtual human.

A novel and economical explanation for SM fermion masses and mixings

Energy Technology Data Exchange (ETDEWEB)

Hernandez, A.E.C. [Universidad Tecnica Federico Santa Maria and Centro Cientifico-Tecnologico de Valparaiso, Valparaiso (Chile)

2016-09-15

I propose the first multiscalar singlet extension of the standard model (SM), which generates tree level top quark and exotic fermion masses as well as one and three loop level masses for charged fermions lighter than the top quark and for light active neutrinos, respectively, without invoking electrically charged scalar fields. That model, which is based on the S{sub 3} x Z{sub 8} discrete symmetry, successfully explains the observed SM fermion mass and mixing pattern. The charged exotic fermions induce one loop level masses for charged fermions lighter than the top quark. The Z{sub 8} charged scalar singlet χ generates the observed charged fermion mass and quark mixing pattern. (orig.)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Energy Technology Data Exchange (ETDEWEB)

Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)

2007-02-15

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

International Nuclear Information System (INIS)

Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.

2007-01-01

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Renormalization group analysis of order parameter fluctuations in fermionic superfluids

International Nuclear Information System (INIS)

Obert, Benjamin

2014-01-01

In this work fluctuation effects in two interacting fermion systems exhibiting fermionic s-wave superfluidity are analyzed with a modern renormalization group method. A description in terms of a fermion-boson theory allows an investigation of order parameter fluctuations already on the one-loop level. In the first project a quantum phase transition between a semimetal and a s-wave superfluid in a Dirac cone model is studied. The interplay between fermions and quantum critical fluctuations close to and at the quantum critical point at zero and finite temperatures are studied within a coupled fermion-boson theory. At the quantum critical point non-Fermi liquid and non-Gaussian behaviour emerge. Close to criticality several quantities as the susceptibility show a power law behaviour with critical exponents. We find an infinite correlation length in the entire semimetallic ground state also away from the quantum critical point. In the second project, the ground state of an s-wave fermionic superfluid is investigated. Here, the mutual interplay between fermions and order parameter fluctuations is studied, especially the impact of massless Goldstone fluctuations, which occur due to spontaneous breaking of the continuous U(1)-symmetry. Fermionic gap and bosonic order parameter are distinguished. Furthermore, the bosonic order parameter is decomposed in transverse and longitudinal fluctuations. The mixing between transverse and longitudinal fluctuations is included in our description. Within a simple truncation of the fermion-boson RG flow, we describe the fermion-boson theory for the first time in a consistent manner. Several singularities appear due the Goldstone fluctuations, which partially cancel due to symmetry. Our RG flow captures the correct infrared asymptotics of the system, where the collective excitations act as an interacting Bose gas. Lowest order Ward identities and the massless Goldstone mode are fulfilled in our truncation.

Adding gauge fields to Kaplan's fermions

International Nuclear Information System (INIS)

Blum, T.; Kaerkkaeinen, L.

1994-01-01

We experiment with adding dynamical gauge field to Kaplan (defect) fermions. In the case of U(1) gauge theory we use an inhomogeneous Higgs mechanism to restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d theory produce the correct 2d gauge dynamics. We measure fermion propagators with dynamical gauge fields. They posses the correct chiral structure. The fermions at the boundary of the support of the gauge field (waveguide) are non-chiral, and have a mass two times heavier than the chiral modes. Moreover, these modes cannot be excited by a source at the defect; implying that they are dynamically decoupled. We have also checked that the anomaly relation is fullfilled for the case of a smooth external gauge field. (orig.)

Searches for Fourth Generation Fermions

Energy Technology Data Exchange (ETDEWEB)

Ivanov, A.; /Fermilab

2011-09-01

We present the results from searches for fourth generation fermions performed using data samples collected by the CDF II and D0 Detectors at the Fermilab Tevatron p{bar p} collider. Many of these results represent the most stringent 95% C. L. limits on masses of new fermions to-date. A fourth chiral generation of massive fermions with the same quantum numbers as the known fermions is one of the simplest extensions of the SM with three generations. The fourth generation is predicted in a number of theories, and although historically have been considered disfavored, stands in agreement with electroweak precision data. To avoid Z {yields} {nu}{bar {nu}} constraint from LEP I a fourth generation neutrino {nu}{sub 4} must be heavy: m({nu}{sub 4}) > m{sub Z}/2, where m{sub Z} is the mass of Z boson, and to avoid LEP II bounds a fourth generation charged lepton {ell}{sub 4} must have m({ell}{sub 4}) > 101 GeV/c{sup 2}. At the same time due to sizeable radiative corrections masses of fourth generation fermions cannot be much higher the current lower bounds and masses of new heavy quarks t' and b' should be in the range of a few hundred GeV/c{sup 2}. In the four-generation model the present bounds on the Higgs are relaxed: the Higgs mass could be as large as 1 TeV/c{sup 2}. Furthermore, the CP violation is significantly enhanced to the magnitude that might account for the baryon asymmetry in the Universe. Additional chiral fermion families can also be accommodated in supersymmetric two-Higgs-doublet extensions of the SM with equivalent effect on the precision fit to the Higgs mass. Another possibility is heavy exotic quarks with vector couplings to the W boson Contributions to radiative corrections from such quarks with mass M decouple as 1/M{sup 2} and easily evade all experimental constraints. At the Tevatron p{bar p} collider 4-th generation chiral or vector-like quarks can be either produced strongly in pairs or singly via electroweak production, where the

Bosonic behavior of entangled fermions

DEFF Research Database (Denmark)

C. Tichy, Malte; Alexander Bouvrie, Peter; Mølmer, Klaus

2012-01-01

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson st......Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi...

Tensor-based spatiotemporal saliency detection

Science.gov (United States)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

Thermal radiation of fermions by an accelerated wall

International Nuclear Information System (INIS)

Horibe, Minoru

1979-01-01

The theory of particle production by an accelerated wall is extended to the massless Dirac particle. It is shown that the mean occupation number of fermions (anti-fermions) is given by the Fermi distribution function. (author)

Simulating an arbitrary number of flavors of dynamical overlap fermions

International Nuclear Information System (INIS)

DeGrand, T.; Schaefer, S.

2006-05-01

We present a set of related Hybrid Monte Carlo methods to simulate an arbitrary number of dynamical overlap fermions. Each fermion is represented by a chiral pseudo-fermion field. The new algorithm reduces critical slowing down in the chiral limit and for sectors of nontrivial topology. (Orig.)

Gauge-invariant dressed fermion propagator in massless QED3

International Nuclear Information System (INIS)

Mitra, Indrajit; Ratabole, Raghunath; Sharatchandra, H.S.

2006-01-01

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED 3 is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement

Exact one-fermion-loop contributions in (1+1)-dimensional solitons

International Nuclear Information System (INIS)

Shepard, J.R.; Price, C.E.; Ferree, T.C.

1993-01-01

We find solutions to the (1+1)-dimensional scalar-only linear σ model. A new method is used to compute one-fermion-loop contributions exactly, and agreemment with published results employing other methods is excellent. A renormalization scheme which differs from that commonly used in such calculations but is similar to that required in 1+3 dimensions is also presented. We compare ''kink'' versus ''shallow bag'' solutions, paying careful attention to the implications of the one-fermion-loop contributions for the stability of the former. We find that, for small fermion multiplicities, self-consistent shallow bag solutions are always more bound than their metastable kink counterparts. However, as the fermion multiplicity increases, shallow bags evolve into kinks which eventually are the only self-consistent configurations. This situation is qualitatively the same for the two renormalization schemes considered. When we construct ''baryons,'' each containing three fermions, the kink configuration is typically more bound than the shallow bag when one-fermion-loop contributions are included

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

1986-01-01

The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

Tensor analysis for physicists

CERN Document Server

Schouten, J A

1989-01-01

This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...

Analysis of Balanced Double Lap Joints with a Bi-Linear Softening Adhesive

DEFF Research Database (Denmark)

Hansen, Christian Skodborg; Stang, Henrik; Schmidt, Jacob Wittrup

2010-01-01

of cracked concrete disks strengthened with adhesive bonded fiber reinforced polymers (FRP), or in any other structure comparable to a double lap joint with a softening interface. The present constitutive model can be changed to fit any model with the same shape of constitutive relationship, see Figure 1.......The response of a bonded symmetric balanced double lap joint under tensile loading with a bilinear softening adhesive is described with a closed form solution. Since bonded joints in concrete structures undergo softening, a versatile model to describe the response for a wide range of constitutive...

Sparse alignment for robust tensor learning.

Science.gov (United States)

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

International Nuclear Information System (INIS)

Huf, P A; Carminati, J

2015-01-01

In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)

Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly

International Nuclear Information System (INIS)

Yoshioka, Nobuyuki; Matsuura, Hiroyasu; Ogata, Masao

2016-01-01

We propose a new physical interpretation of the Diophantine equation of σ xy for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called 'subcells', which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of σ xy , that are consistent with the Diophantine equation: Landau quantization of (1) massless Dirac fermions or (2) free fermions in Hofstadter's butterfly. (author)

Wigner functions for fermions in strong magnetic fields

Science.gov (United States)

Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

2018-02-01

We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

Hierarchy spectrum of SM fermions: from top quark to electron neutrino

International Nuclear Information System (INIS)

Xue, She-Sheng

2016-01-01

In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy functions. The study is motivated by the speculation that these four-fermion operators are probably originated due to the quantum gravity, which provides the natural regularization for chiral-symmetric gauge field theories. In the chiral-gauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the top-quark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the top-quark mass, four-fermion interactions and fermion-flavor mixing matrices. A phase transition from the symmetry breaking phase to the chiral-gauge symmetric phase at TeV scale occurs and the drastically fine-tuning problem can be resolved. In the infrared fixed-point domain of the four-fermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and family-flavor mixing matrices with three additional right-handed neutrinos ν_R"f. Large Majorana masses and lepton-number symmetry breaking are originated by the four-fermion interactions among ν_R"f and their left-handed conjugated fields ν_R"f"c. Light masses of gauged Majorana neutrinos in the normal hierarchy (10"−"5−10"−"2 eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forward-backward asymmetry of tt̄-production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).

Hierarchy spectrum of SM fermions: from top quark to electron neutrino

Energy Technology Data Exchange (ETDEWEB)

Xue, She-Sheng [ICRANet,Piazza della Repubblica 10, 65122 Pescara (Italy); Physics Department, Sapienza University of Rome,Piazzale Aldo Moro 5, 00185 Roma (Italy)

2016-11-10

In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy functions. The study is motivated by the speculation that these four-fermion operators are probably originated due to the quantum gravity, which provides the natural regularization for chiral-symmetric gauge field theories. In the chiral-gauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the top-quark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the top-quark mass, four-fermion interactions and fermion-flavor mixing matrices. A phase transition from the symmetry breaking phase to the chiral-gauge symmetric phase at TeV scale occurs and the drastically fine-tuning problem can be resolved. In the infrared fixed-point domain of the four-fermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and family-flavor mixing matrices with three additional right-handed neutrinos ν{sub R}{sup f}. Large Majorana masses and lepton-number symmetry breaking are originated by the four-fermion interactions among ν{sub R}{sup f} and their left-handed conjugated fields ν{sub R}{sup fc}. Light masses of gauged Majorana neutrinos in the normal hierarchy (10{sup −5}−10{sup −2} eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forward-backward asymmetry of tt̄-production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).

Unique characterization of the Bel-Robinson tensor

International Nuclear Information System (INIS)

Bergqvist, G; Lankinen, P

2004-01-01

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors

Fermion field as inflaton, dark energy and dark matter

International Nuclear Information System (INIS)

Grams, Guilherme; Souza, Rudinei C de; Kremer, Gilberto M

2014-01-01

The search for constituents that can explain the periods of accelerating expansion of the Universe is a fundamental topic in cosmology. In this context, we investigate how fermionic fields minimally and non-minimally coupled with the gravitational field may be responsible for accelerated regimes during the evolution of the Universe. The forms of the potential and coupling of the model are determined through the technique of the Noether symmetry for two cases. The first case comprises a Universe filled only with the fermion field. Cosmological solutions are straightforwardly obtained for this case and an exponential inflation mediated by the fermion field is possible with a non-minimal coupling. The second case takes account of the contributions of radiation and baryonic matter in the presence of the fermion field. In this case the fermion field plays the role of dark energy and dark matter, and when a non-minimal coupling is allowed, it mediates a power-law inflation. (paper)

Majorana and Majorana-Weyl fermions in lattice gauge theory

International Nuclear Information System (INIS)

Inagaki, Teruaki; Suzuki, Hiroshi

2004-01-01

In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factorized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find. (author)

Hybrid Monte Carlo algorithm with fat link fermion actions

International Nuclear Information System (INIS)

Kamleh, Waseem; Leinweber, Derek B.; Williams, Anthony G.

2004-01-01

The use of APE smearing or other blocking techniques in lattice fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as flat link irrelevant clover (FLIC) fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarization is often performed using an iterative maximization of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants. The necessary equations of motion for FLIC fermions are derived, and some initial simulation results are presented. The technique is more general however, and is straightforwardly applicable to other smearing techniques or fat link actions

Light fermions in quantum gravity

International Nuclear Information System (INIS)

Eichhorn, Astrid; Gies, Holger

2011-01-01

We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. Specifically we address the question of whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional renormalization group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we found that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaußian fixed point generically admits universes with light fermions. Our results thus further support quantum gravity theories built on fluctuations of the metric field such as the asymptotic-safety scenario. A study of chiral symmetry breaking through gravitational quantum effects may also serve as a significant benchmark test for other quantum gravity scenarios, since a completely broken chiral symmetry at the Planck scale would not be in accordance with the observation of light fermions in our universe. We demonstrate that this elementary observation already imposes constraints on a generic UV completion of gravity. (paper)

Symmetry between bosons and fermions

International Nuclear Information System (INIS)

Ohnuki, Y.; Kamefuchi, S.

1986-01-01

By definition Bosons and Fermions behave quite differently as regards statistics. It is equally true, however, that in some other respects they do behave similarly or even symmetrically. In the present paper they would like to show that such similarity or symmetry can be exhibited most fully when the theory is formulated in a specific manner, i.e. in terms of annihilation and creation operators a/sub j/ and a/sub j//sup dagger/ or what they term g-numbers. The difference between Bosons and Fermions can, of course, be traced back to the difference in the signatures (jj) = +,- attached to the brackets in the basic commutation relations: [a/sub j/,a/sub j//sup dagger/]-(jj) = 1, [a/sub j/,a/sub j/]-(jj) = 0. However, the substantial part of the theory can in fact be formulated without specifying the individual signatures (jj). This is why it is possible to treat Bosons and Fermions in a unified manner, and to thereby consider, among the two, super- or more general, g-symmetry transformations. 6 references, 1 table

Grassmann phase space methods for fermions. II. Field theory

Energy Technology Data Exchange (ETDEWEB)

Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)

2017-02-15

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

Grassmann phase space methods for fermions. II. Field theory

International Nuclear Information System (INIS)

Dalton, B.J.; Jeffers, J.; Barnett, S.M.

2017-01-01

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

Interacting-string picture of the fermionic string

International Nuclear Information System (INIS)

Mandelstam, S.

1986-01-01

This report gives a review of the interacting-string picture of the Bose string. In the present lecture, the author outlines a similar treatment of the Fermionic string. The quantization of the free Fermionic string is carried out to the degrees of freedom x, representing the displacement of the string. Also presented are Grassman degrees of freedom S distributed along the string. The report pictures the fermionic string as a string of dipoles. The general picture of the interaction of such strings by joining and splitting is the same as for the Bose string. The author does not at present have the simplest formula for fermion string scattering amplitudes. A less detailed treatment is given than for the Bose string. The report sets up the functional-integration formalism, derives the analog mode, and indicates in general, terms how the conformal transformation to the z-plane may be performed. The paper concludes by stating without proof the formula for the N-article tree amplitude in the manifestly supersymmetric formalism

Evaluating the fermionic determinant of dynamical configurations

International Nuclear Information System (INIS)

Hasenfratz, Anna; Alexandru, Andrei

2002-01-01

We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of the ratios of fermionic determinants is essential for a recently proposed updating method of smeared link dynamical fermions. This update creates a sequence of configurations by changing a subset of the gauge links by a pure gauge heat bath or over-relaxation step. The acceptance of the proposed configuration depends on the ratio of the fermionic determinants on the new and original configurations. We study this ratio as a function of the number of links that are changed in the heat bath update. We find that even when every link of a given direction and parity of a 10 fm 4 configuration is updated, the average of the determinant ratio is still close to one and with the improved stochastic estimator the proposed change is accepted with about 20% probability. This improvement suggests that the new updating technique can be efficient even on large lattices and could provide an updating method for dynamical overlap actions

Anomalous diffusion of fermions in superlattices

International Nuclear Information System (INIS)

Drozdz, S.; Okolowicz, J.; Srokowski, T.; Ploszajczak, M.

1996-03-01

Diffusion of fermions in the periodic two-dimensional lattice of fermions is studied. It is shown that effects connected with antisymmetrization of the wave function increase chaoticness of motion. Various types of anomalous diffusion, characterized by a power spectral analysis are found. The nonlocality of the Pauli potential destroys cantori in the phase space. Consequently, the diffusion process is dominated by long free paths and the power spectrum is logarithmic at small frequency limit. (author)

Tensor Product of Polygonal Cell Complexes

OpenAIRE

Chien, Yu-Yen

2017-01-01

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Variable-coefficient higher-order nonlinear Schroedinger model in optical fibers: Variable-coefficient bilinear form, Baecklund transformation, brightons and symbolic computation

International Nuclear Information System (INIS)

Tian Bo; Gao Yitian; Zhu Hongwu

2007-01-01

Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear Schroedinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical communication systems with distributed dispersion and nonlinearity management. Of physical and optical interests, with bilinear method extend, the vcHNLS model is transformed into a variable-coefficient bilinear form, and then an auto-Baecklund transformation is constructed. Constraints on coefficient functions are analyzed. Potentially observable with future optical-fiber experiments, variable-coefficient brightons are illustrated. Relevant properties and features are discussed as well. Baecklund transformation and other results of this Letter will be of certain value to the studies on inhomogeneous fiber media, core of dispersion-managed brightons, fiber amplifiers, laser systems and optical communication links with distributed dispersion and nonlinearity management

Ladder physics in the spin fermion model

Science.gov (United States)

Tsvelik, A. M.

2017-05-01

A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. It is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d -Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.

Ladder physics in the spin fermion model

International Nuclear Information System (INIS)

Tsvelik, A. M.

2017-01-01

A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. Here, it is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.

Functional approach without path integrals to finite temperature free fermions

International Nuclear Information System (INIS)

Souza, S.M. de; Santos, O. Rojas; Thomaz, M.T.

1999-01-01

Charret et al applied the properties of Grassmann generators to develop a new method to calculate the coefficients of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d ≥1). The methodology explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. we apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the β-independent and μindependent infinities that plague the continuum path integral formulation. (author)

Notes on super Killing tensors

Energy Technology Data Exchange (ETDEWEB)

Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)

2016-03-14

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

The GL(1 vertical stroke 1)-symplectic fermion correspondence

International Nuclear Information System (INIS)

Creutzig, Thomas; Roenne, Peter B.

2008-12-01

In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)

The GL(1 vertical stroke 1)-symplectic fermion correspondence

Energy Technology Data Exchange (ETDEWEB)

Creutzig, Thomas; Roenne, Peter B.

2008-12-15

In this note we prove a correspondence between the Wess-Zumino-Novikov-Witten model of the Lie supergroup GL(1 vertical stroke 1) and a free model consisting of two scalars and a pair of symplectic fermions. This model was discussed earlier by LeClair. Vertex operators for the symplectic fermions include twist fields, and correlation functions of GL(1 vertical stroke 1) agree with the known results for the scalars and symplectic fermions. We perform a detailed study of boundary states for symplectic fermions and apply them to branes in GL(1 vertical stroke 1). This allows us to compute new amplitudes of strings stretching between branes of different types and confirming Cardy's condition. (orig.)

A bilinear elastic constitutive model applied for midpalatal suture behavior during rapid maxillary expansion

Directory of Open Access Journals (Sweden)

Larissa Carvalho Trojan Serpe

Full Text Available Introduction : This study aims to evaluate the influence of the biomechanical behavior of the midpalatal suture (MPS during the rapid maxillary expansion (RME when modeled by the Finite Element Method. Methods Four simulation alternatives are discussed and, for each analysis, the suture is considered as a functional unit with a different mechanical behavior: (i without MPS elements, (ii MPS with Young's modulus (E equal to 1 MPa, (ii MPS with E equal to 0.01 MPa and (iv MPS with bilinear elastic behavior. Results The stress analysis showed that, when MPS is not considered in the model, stress peaks are reduced in magnitude and their distribution is restricted to a smaller area when compared to the model with the inclusion of MPS (E=1 MPa. The increased suture stiffness also has a direct influence on MPS displacements after 30 expander activations. Conclusion The consideration of the MPS in RME computer models influences greatly the calculated displacements between the suture bone ends, even as the stress levels in maxillary structures. Furthermore, as proposed for the described model, the elastic bilinear behavior assigned to MPS allows coherent prediction of stresses and displacements results, being a good representation for this suture overall behavior.

Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states

Science.gov (United States)

He, Pan; Zhang, Steven S.-L.; Zhu, Dapeng; Liu, Yang; Wang, Yi; Yu, Jiawei; Vignale, Giovanni; Yang, Hyunsoo

2018-05-01

Surface states of three-dimensional topological insulators exhibit the phenomenon of spin-momentum locking, whereby the orientation of an electron spin is determined by its momentum. Probing the spin texture of these states is of critical importance for the realization of topological insulator devices, but the main technique currently available is spin- and angle-resolved photoemission spectroscopy. Here we reveal a close link between the spin texture and a new kind of magnetoresistance, which depends on the relative orientation of the current with respect to the magnetic field as well as the crystallographic axes, and scales linearly with both the applied electric and magnetic fields. This bilinear magnetoelectric resistance can be used to map the spin texture of topological surface states by simple transport measurements. For a prototypical Bi2Se3 single layer, we can map both the in-plane and out-of-plane components of the spin texture (the latter arising from hexagonal warping). Theoretical calculations suggest that the bilinear magnetoelectric resistance originates from conversion of a non-equilibrium spin current into a charge current under application of the external magnetic field.

Physics of heavy fermions heavy fermions and strongly correlated electrons systems

CERN Document Server

Onuki, Yoshichika

2018-01-01

A large variety of materials prove to be fascinating in solid state and condensed matter physics. New materials create new physics, which is spearheaded by the international experimental expert, Prof Yoshichika Onuki. Among them, the f electrons of rare earth and actinide compounds typically exhibit a variety of characteristic properties, including spin and charge orderings, spin and valence fluctuations, heavy fermions, and anisotropic superconductivity. These are mainly manifestations of better competitive phenomena between the RKKY interaction and the Kondo effect. The present text is written so as to understand these phenomena and the research they prompt. For example, superconductivity was once regarded as one of the more well-understood many-body problems. However, it is, in fact, still an exciting phenomenon in new materials. Additionally, magnetism and superconductivity interplay strongly in heavy fermion superconductors. The understanding of anisotropic superconductivity and magnetism is a challengin...

Tensor Train Neighborhood Preserving Embedding

Science.gov (United States)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Fermions and vortex solutions in Abelian and non-Abelian gauge theories

International Nuclear Information System (INIS)

de Vega, H.J.

1978-01-01

The interaction of fermions with an extended vortex solution of the Higgs model is investigated. It is found that this interaction has long-range inverse-square tail. It is caused by the coupling of the fermion angular momentum with the vortex gauge field itself. The fermion-vortex bound states present at the threshold and the fermion-vortex scattering are studied. The scattering phase shifts and the Jost functions are obtained for large and small fermion momenta as well as the low-energy cross section which diverges at zero momentum. The quantum field theory in the one-vortex sectors is developed. It is found that, in the presence of fermions, a vortex with an even (odd) number of flux quanta has a half-integer (integer) fermionic number. It follows that a two-quantum vortex is stable. Finally, the stable vortex solution of an SU(2) Higgs model is investigated. The appropriate ansatz for the field is given and radial equations are discussed. It is shown that the interaction of a vortex with any nonsinglet particle has a long-range inverse-square tail

Improved continuum limit lattice action for QCD with Wilson fermions

International Nuclear Information System (INIS)

Sheikholeslami, B.; Wohlert, R.

1985-03-01

Two possible ways of extending Symanzik's improvement programme to lattice fermions namely improvement to first and second order in the lattice spacing 'a' are discussed. The corresponding lattice actions for fermions are constructed and tree level improvement conditions are derived by considering classical improvement. The concept of on shell improvement is generalized to the lattice fermions studied here and the free parameters are determined for O(a) and O(a 2 ) on shell improved actions to all orders of perturbation theory. No evidence is found that the complicated structure of the O(a 2 ) on shell improved action especially the arising fermion contact terms can be removed beyond tree level. The effect of terms in the action that explicitly break chiral symmetry and therefore remove the phenomenon of species doubling are investigated by considering the energy momentum relations of the arising tree level improved actions. Our main result is that the O(a) improved action is a slightly modified Wilson fermion action which can still be written with only nearest neighbour fermion interactions. (orig.)

Quarks and leptons as quasi Nambu-Goldstone fermions

International Nuclear Information System (INIS)

Buchmueller, W.; Peccei, R.D.; Yanagida, T.

1983-01-01

We discuss a new idea for constructing composite quarks and leptons which have (approximately) vanishing mass. They are associated with fermionic partners of Goldstone bosons arising from the spontaneous breakdown of an internal symmetry Gsub(f) in a supersymmetric preon theory. For Gsub(f)=SU(5) being broken to SU(3) x U(1)sub(em) there arise as quasi Goldstone fermions, naturally and unequivocally, precisely the quarks and leptons of one family. The dynamics of these quasi Goldstone fermions is explored by constructing a general supersymmetric nonlinear effective lagrangian. By means of a reduced model, we show that the first nontrivial interactions of the quasi Goldstone fermions can give rise, in an effective way, to the weak interactions. Issues connected with the incorporation of families in the scheme and the generation of masses, as well as the possible structure of the underlying preon theory are briefly discussed. (orig.)

The Topology of Symmetric Tensor Fields

Science.gov (United States)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

The effective action for chiral fermions

International Nuclear Information System (INIS)

Alvarez-Gaume, L.

1985-01-01

This paper reports on recent work which given an exact characterization of the imaginary part of the effective action for chiral fermions in 2n dimensions in terms of the spectral asymmetry of a suitable (2n+1)-dimensional operator. In order to keep the discussion as simple as possible, the author concentrates on four dimensional fermions with arbitrary external gauge fields. This approach can be extended without difficulty to higher dimensions and also to include external gravitational fields

A group property for the coherent state representation of fermionic squeezing operators

Science.gov (United States)

Fan, Hong-yi; Li, Chao

2004-06-01

For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.

A group property for the coherent state representation of fermionic squeezing operators

International Nuclear Information System (INIS)

Fan Hongyi; Li Chao

2004-01-01

For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation

Improved formulation of GNO fermionization theorem

International Nuclear Information System (INIS)

Fre, P.; Gliozzi, F.; Piras, A.

1989-01-01

It is pointed out that in the Kac-Moody algebras fulfilling the fermionization criterion of Goddard, Nahm and Olive and having a non-minimal value of the central charge κ, only a proper subset of the allowed unitary highest weight representations can actually be encoded in a free fermion theory. These truly fermionizable representations are selected by a very specific non-regular embedding of the fermionizable Kac-Moody algebra into the lowest level SO(N F ) Kac-Moody algebra, N F being both the number of fermions and the dimension of the GNO symmetric space. This embedding is a particular case of the embeddings considered by Bais and Bouwknegt and by Schellekens and Warner, for which the Virasoro central charge of the subgroup is equal to that of the group. Furthermore, these fermionizable representations span an orbit of the modular group always leading to a non-trivial modular invariant partition function

Derivation of mean-field dynamics for fermions

International Nuclear Information System (INIS)

Petrat, Soeren

2014-01-01

In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works, the mean-field limit is usually either coupled to a semiclassical limit, or the interaction is scaled down so much, that the system behaves freely for large particle number N. We mainly consider systems with total kinetic energy bounded by const.N and long-range interaction potentials, e.g., Coulomb interaction. Examples for such systems are large molecules or certain solid states. Our analysis also applies to attractive interactions, as, e.g., in fermionic stars. The fermionic Hartree(-Fock) equations are a standard tool to describe, e.g., excited states or chemical reactions of large molecules (like proteins). A deeper understanding of these equations as an approximation to the time evolution of a many body quantum system is thus highly relevant. We consider the fermionic Hartree equations (i.e., the Hartree-Fock equations without exchange term) in this work, since the exchange term is subleading in our setting. The main result is that the fermionic Hartree dynamics approximates the Schroedinger dynamics well for large N. This statement becomes exact in the thermodynamic limit N→∞. We give explicit values for the rates of convergence. We prove two types of results. The first type is very general and concerns arbitrary free Hamiltonians (e.g., relativistic, non-relativistic, with external fields) and arbitrary interactions. The theorems give explicit conditions on the solutions to the fermionic Hartree equations under which a derivation of the mean-field dynamics succeeds. The second type of results scrutinizes situations where the conditions are fulfilled. These results are about non-relativistic free Hamiltonians with external fields, systems with total kinetic energy bounded by const.N and with long-range interactions of

Diffusion in higher dimensional SYK model with complex fermions

Science.gov (United States)

Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

2018-01-01

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

Boson-fermion mixtures inside an elongated cigar-shaped trap

International Nuclear Information System (INIS)

Akdeniz, Z; Vignolo, P; Tosi, M P

2005-01-01

We present mean-field calculations of the equilibrium state in a gaseous mixture of bosonic and spin-polarized fermionic atoms with repulsive or attractive interspecies interactions, confined inside a cigar-shaped trap under conditions such that the radial thickness of the two atomic clouds is approaching the magnitude of the s-wave scattering lengths. In this regime, the kinetic pressure of the fermionic component is dominant. Full demixing under repulsive boson-fermion interactions can occur only when the number of fermions in the trap is below a threshold, and collapse under attractive interactions is suppressed within the range of validity of the mean-field model. Specific numerical illustrations are given for values of system parameters obtaining in 7 Li- 6 Li clouds

Massless fermions and Kaluza--Klein theory with torsion

International Nuclear Information System (INIS)

Wu, Y.; Zee, A.

1984-01-01

A pure Kaluza--Klein theory contains no massless fermion in four-dimensional theory. We investigate the effect of introducing torsion on the internal manifold and find that there are massless fermions. The hope is that given an isometry group the representation to which these fermions belong is fixed, in contrast to the situation in Yang--Mills theory. We show that this is indeed the case, but the representations do not appear to be the ones favored by current theoretical prejudice. The cases with parallelizable torsions on a group manifold as the internal manifold are analyzed in detail

Chiral anomaly, fermionic determinant and two dimensional models

International Nuclear Information System (INIS)

Rego Monteiro, M.A. do.

1985-01-01

The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt

Random SU(2) invariant tensors

Science.gov (United States)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

Coupled fermion-kink system in Jackiw-Rebbi model

International Nuclear Information System (INIS)

Amado, A.; Mohammadi, A.

2017-01-01

In this paper, we study Jackiw-Rebbi model, in which a massless fermion is coupled to the kink of λφ"4 theory through a Yukawa interaction. In the original Jackiw-Rebbi model, the soliton is prescribed. However, we are interested in the back-reaction of the fermion on the soliton besides the effect of the soliton on the fermion. Also, as a particular example, we consider a minimal supersymmetric kink model in (1 + 1) dimensions. In this case, the bosonic self-coupling, λ, and the Yukawa coupling between fermion and soliton, g, have a specific relation, g = √(λ/2). As the set of coupled equations of motion of the system is not analytically solvable, we use a numerical method to solve it self-consistently. We obtain the bound energy spectrum, bound states of the system and the corresponding shape of the soliton using a relaxation method, except for the zero mode fermionic state and threshold energies which are analytically solvable. With the aid of these results, we are able to show how the soliton is affected in general and supersymmetric cases. The results we obtain are consistent with the ones in the literature, considering the soliton as background. (orig.)

Continuum-limit scaling of overlap fermions as valence quarks

International Nuclear Information System (INIS)

Cichy, Krzysztof; Herdoiza, Gregorio; Jansen, Karl

2009-10-01

We present the results of a mixed action approach, employing dynamical twisted mass fermions in the sea sector and overlap valence fermions, with the aim of testing the continuum limit scaling behaviour of physical quantities, taking the pion decay constant as an example. To render the computations practical, we impose for this purpose a fixed finite volume with lattice size L∼1.3 fm. We also briefly review the techniques we have used to deal with overlap fermions. (orig.)

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Improved tensor multiplets

International Nuclear Information System (INIS)

Wit, B. de; Rocek, M.

1982-01-01

We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)

The evolution of tensor polarization

International Nuclear Information System (INIS)

Huang, H.; Lee, S.Y.; Ratner, L.

1993-01-01

By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake

Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

CERN Document Server

Itskov, Mikhail

2015-01-01

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Bragg diffraction of fermions at optical potentials

International Nuclear Information System (INIS)

Deh, Benjamin

2008-01-01

This thesis describes the Bragg diffraction of ultracold fermions at an optical potential. A moving optical lattice was created, by overlaying two slightly detuned lasers. Atoms can be diffracted at this lattice if the detuning fulfills the Bragg condition for resting atoms. This Bragg diffraction is analyzed systematically in this thesis. To this end Rabi oscillations between the diffraction states were driven, as well in the weakly interacting Bragg regime, as in the strongly interacting Kapitza-Dirac regime. Simulations, based on a driven two-, respectively multilevel-system describe the observed effects rather well. Furthermore, the temporal evolution of the diffracted states in the magnetic trapping potential was studied. The anharmonicity of the trap in use and the scattering cross section for p-wave collisions in a 6 Li system was determined from the movement of these states. Moreover the momentum distribution of the fermions was measured with Bragg spectroscopy and first signs of Fermi degeneracy were found. Finally an interferometer with fermions was build, exhibiting a coherence time of more than 100 μs. With this, the possibility for measurement and manipulation of ultracold fermions with Bragg diffraction could bee shown. (orig.)

The chirally rotated Schroedinger functional. Theoretical expectations and perturbative tests

International Nuclear Information System (INIS)

Dalla Brida, Mattia

2016-03-01

The chirally rotated Schroedinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schroedinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Fermion determinants in lattice QCD

International Nuclear Information System (INIS)

Johnson, Christopher Andrew

2001-01-01

The main topic of this thesis concerns efficient algorithms for the calculation of determinants of the kind of matrix typically encountered in lattice QCD. In particular an efficient method for calculating the fermion determinant is described. Such a calculation is useful to illustrate the effects of light dynamical (virtual) quarks. The methods employed in this thesis are stochastic methods, based on the Lanczos algorithm, which is used for the solution of large, sparse matrix problems via a partial tridiagonalisation of the matrix. Here an implementation is explored which requires less exhaustive treatment of the matrix than previous Lanczos methods. This technique exploits the analogy between the Lanczos tridiagonalisation algorithm and Gaussian quadrature in order to calculate the fermion determinant. A technique for determining a number of the eigenvalues of the matrix is also presented. A demonstration is then given of how one can improve upon this estimate considerably using variance reduction techniques, reducing the variance by a factor of order 100 with a further, equal amount of work. The variance reduction method is a two-stage process, involving a Chebyshev approximation to the quantity in question and then the subtraction of traceless operators. The method is applied to the fermion determinant for non-perturbatively improved Wilson fermions on a 16 3 x 32 lattice. It is also applicable to a wider class of matrix operators. Finally we discuss how dynamical quark effects may be simulated in a Monte Carlo process with an effective partitioning of low and high eigenmodes. This may be done via selective updating of a trial configuration which highlights the physically relevant effects of light quark modes. (author)

Fermionic covariant prolongation structure theory for supernonlinear evolution equation

International Nuclear Information System (INIS)

Cheng Jipeng; Wang Shikun; Wu Ke; Zhao Weizhong

2010-01-01

We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schroedinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Baecklund transformation.

Quantum computing with Majorana fermion codes

Science.gov (United States)

Litinski, Daniel; von Oppen, Felix

2018-05-01

We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero-time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local 4-Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few-Majorana parity measurements. To this end, we discuss twist defects in Majorana fermion surface codes and adapt the technique of twist-based lattice surgery to fermionic codes. Moreover, we propose a family of codes that we refer to as Majorana color codes, which are obtained by concatenating Majorana surface codes with small Majorana fermion codes. Majorana surface and color codes can be used to decrease the space overhead and stabilizer weight compared to their bosonic counterparts.

Link prediction via generalized coupled tensor factorisation

DEFF Research Database (Denmark)

Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.

2012-01-01

and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....

Fermions and link invariants

International Nuclear Information System (INIS)

Kauffman, L.; Saleur, H.

1991-01-01

Various aspects of knot theory are discussed when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. It is discussed how the R matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group U q gl(1,1). New families of solutions of the Yang Baxter equation obtained from ''linear'' representations of the braid group and exterior algebra are investigated. State models associated with U q sl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial are studied. Invariants of links in solid handlebodies are considered and it is shown how the non trivial topology lifts the boson fermion degeneracy is present in S 3 . (author) 36 refs

The physics and chemistry of heavy Fermions

International Nuclear Information System (INIS)

Fisk, Z.; Sarrao, J.L.

1994-01-01

The heavy Fermions are a subset of the f-element intermetallics straddling the magnetic/non-magnetic boundary. Their low temperature properties are characterized by an electronic energy scale of order 1--10 K. Among the low temperature ground states observed in heavy Fermion compounds are exotic superconductors and magnets, as well as unusual semiconductors. We review here the current experimental and theoretical understanding of these systems

Fermion interactions with a Kaluza-Klein dyon

International Nuclear Information System (INIS)

Xi, Z.M.

1986-04-01

The fermion dynamics in the background of a five-dimensional Kaluza-Klein dyon is studied. It is found that the hamiltonian is self-adjoint despite the singular nature of the origin, and the fermion scattering on the dyon in the lowest angular momentum j = 0 channel is a helicity flip process. The possibility for charge-exchange process in the non-Abelian Kaluza-Klein theories is discussed

Energy-momentum tensor of the electromagnetic field

International Nuclear Information System (INIS)

Horndeski, G.W.; Wainwright, J.

1977-01-01

In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources

Gauge-invariant dressed fermion propagator in massless QED{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Mitra, Indrajit [Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan-Nagar, Kolkata 700064 (India)]. E-mail: indrajit.mitra@saha.ac.in; Ratabole, Raghunath [Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India)]. E-mail: raghu@imsc.res.in; Sharatchandra, H.S. [Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India)]. E-mail: sharat@imsc.res.in

2006-04-27

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED{sub 3} is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.

Two-loop fermionic corrections to massive Bhabha scattering

Energy Technology Data Exchange (ETDEWEB)

Actis, S.; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Czakon, M. [Wuerzburg Univ. (Germany). Inst. fuer Theoretische Physik und Astrophysik]|[Institute of Nuclear Physics, NSCR DEMOKRITOS, Athens (Greece); Gluza, J. [Silesia Univ., Katowice (Poland). Inst. of Physics

2007-05-15

We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses m{sub e}, m{sub f} and the Mandelstam invariants s, t, u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales m{sup 2}{sub e}<fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions. (orig.)

Four-fermion simulation at LEP2 in DELPHI

CERN Document Server

Ballestrero, A; Cossutti, F; Migliore, E

2003-01-01

We present and discuss the generator setup for $e^+e^-\\rightarrow 4f$ processes chosen by the DELPHI collaboration. The need to combine the most recent theoretical achievements in the CC03 sector with the state of the art description of the remaining part of the 4-fermion processes has led to an original combination of different codes, with the {\\tt WPHACT 2.0} 4-fermion generator and the {\\tt YFSWW} code for the CC03 $\\mathcal{O}(\\alpha)$ corrections as a starting point. The coverage of the 4-fermion phase space is discussed in detail, with particular attention to ensuring the compatibility of {\\tt WPHACT} with dedicated $\\gamma\\gamma$ generators.

Fermionic formula for double Kostka polynomials

OpenAIRE

Liu, Shiyuan

2016-01-01

The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\\Bla,\\Bmu}(t),$ indexed by two double partitions $\\Bla,\\Bmu,$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{\\Bla,\\Bmu}(t)$ in the special case where $\\Bmu=(-,\\mu'').$ We formula...

A new Weyl-like tensor of geometric origin

Science.gov (United States)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Tensor calculus for physics a concise guide

CERN Document Server

Neuenschwander, Dwight E

2015-01-01

Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...

Bilinear modeling of EMG signals to extract user-independent features for multiuser myoelectric interface.

Science.gov (United States)

Matsubara, Takamitsu; Morimoto, Jun

2013-08-01

In this study, we propose a multiuser myoelectric interface that can easily adapt to novel users. When a user performs different motions (e.g., grasping and pinching), different electromyography (EMG) signals are measured. When different users perform the same motion (e.g., grasping), different EMG signals are also measured. Therefore, designing a myoelectric interface that can be used by multiple users to perform multiple motions is difficult. To cope with this problem, we propose for EMG signals a bilinear model that is composed of two linear factors: 1) user dependent and 2) motion dependent. By decomposing the EMG signals into these two factors, the extracted motion-dependent factors can be used as user-independent features. We can construct a motion classifier on the extracted feature space to develop the multiuser interface. For novel users, the proposed adaptation method estimates the user-dependent factor through only a few interactions. The bilinear EMG model with the estimated user-dependent factor can extract the user-independent features from the novel user data. We applied our proposed method to a recognition task of five hand gestures for robotic hand control using four-channel EMG signals measured from subject forearms. Our method resulted in 73% accuracy, which was statistically significantly different from the accuracy of standard nonmultiuser interfaces, as the result of a two-sample t -test at a significance level of 1%.

Seamless warping of diffusion tensor fields

DEFF Research Database (Denmark)

Xu, Dongrong; Hao, Xuejun; Bansal, Ravi

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...

Fermion mass hierarchies in theories of technicolor

International Nuclear Information System (INIS)

Peskin, M.E.

1981-01-01

Models in which light fermion masses result from dynamical symmetry breaking often produce these masses in a hierarchial pattern. The author exhibits two scenarios for obtaining such hierarchies and illustrates each with a simple model of mass generation. In the first scenario, the light fermion masses are separated by powers of a weak coupling constant; in the second scenario, they are separated by a ratio of large mass scales

Anomalous fermion number nonconservation: Paradoxes in the level crossing picture

International Nuclear Information System (INIS)

Burnier, Y.

2006-01-01

In theories with anomalous fermion number nonconservation, the level-crossing picture is considered a faithful representation of the fermionic quantum number variation. It represents each created fermion by an energy level that crosses the zero-energy line from below. If several fermions of various masses are created, the level-crossing picture contains several levels that cross the zero-energy line and cross each other. However, we know from quantum mechanics that the corresponding levels cannot cross if the different fermions are mixed via some interaction potential. The simultaneous application of these two requirements on the level behavior leads to paradoxes. For instance, a naive interpretation of the resulting level-crossing picture gives rise to charge nonconservation. In this paper, we resolve this paradox by a precise calculation of the transition probability, and discuss what are the implications for the electroweak theory. In particular, the nonperturbative transition probability is higher if top quarks are present in the initial state

Tensor norms and operator ideals

CERN Document Server

Defant, A; Floret, K

1992-01-01

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer

Effective Mass and g Factor of Four-Flux-Quanta Composite Fermions

International Nuclear Information System (INIS)

Yeh, A.S.; Tsui, D.C.; Stormer, H.L.; Pfeiffer, L.N.; Baldwin, K.W.; West, K.W.; Stormer, H.L.; Tsui, D.C.

1999-01-01

We investigate the properties of composite fermions with four attached flux quanta through tilted-field experiments near Landau level filling factor ν=3/4 . The observed collapse of fractional quantum Hall gaps in the vicinity of this quarter-filling state can be comprehensively understood in terms of composite fermions with mass and spin. Remarkably, the effective mass and g factor of these four-flux-quanta composite fermions around ν=3/4 are very similar to those of two-flux-quanta composite fermions around ν=3/2 . copyright 1999 The American Physical Society

Projective flatness in the quantisation of bosons and fermions

Science.gov (United States)

Wu, Siye

2015-07-01

We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.

Shape anisotropy: tensor distance to anisotropy measure

Science.gov (United States)

Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.

2011-03-01

Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

Certificateless Key-Insulated Generalized Signcryption Scheme without Bilinear Pairings

Directory of Open Access Journals (Sweden)

Caixue Zhou

2017-01-01

Full Text Available Generalized signcryption (GSC can be applied as an encryption scheme, a signature scheme, or a signcryption scheme with only one algorithm and one key pair. A key-insulated mechanism can resolve the private key exposure problem. To ensure the security of cloud storage, we introduce the key-insulated mechanism into GSC and propose a concrete scheme without bilinear pairings in the certificateless cryptosystem setting. We provide a formal definition and a security model of certificateless key-insulated GSC. Then, we prove that our scheme is confidential under the computational Diffie-Hellman (CDH assumption and unforgeable under the elliptic curve discrete logarithm (EC-DL assumption. Our scheme also supports both random-access key update and secure key update. Finally, we evaluate the efficiency of our scheme and demonstrate that it is highly efficient. Thus, our scheme is more suitable for users who communicate with the cloud using mobile devices.

Fermion fields in η-ξ spacetime

International Nuclear Information System (INIS)

Gui, Y.

1992-01-01

Fermion fields in η-ζ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in η-ζ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in η-ζ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in η-ζ spacetime originates from Lorentz transformation properties of the fields

Holographic fermionic spectrum from Born–Infeld AdS black hole

Directory of Open Access Journals (Sweden)

Jian-Pin Wu

2016-07-01

Full Text Available In this letter, we systematically explore the holographic (non-relativistic fermionic spectrum without/with dipole coupling dual to Born–Infeld anti-de Sitter (BI-AdS black hole. For the relativistic fermionic fixed point, this holographic fermionic system exhibits non-Fermi liquid behavior. Also, with the increase of BI parameter γ, the non-Fermi liquid becomes even “more non-Fermi”. When the dipole coupling term is included, we find that the BI term makes it a lot tougher to form the gap. While for the non-relativistic fermionic system with large dipole coupling in BI-AdS background, with the increase of BI parameter, the gap comes into being again.

Tensors and their applications

CERN Document Server

Islam, Nazrul

2006-01-01

About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces

Tensor Completion Algorithms in Big Data Analytics

OpenAIRE

Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia

2017-01-01

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...

Efficient MATLAB computations with sparse and factored tensors.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

2006-12-01

In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

Singlet fermionic dark matter with Veltman conditions

Science.gov (United States)

Kim, Yeong Gyun; Lee, Kang Young; Nam, Soo-hyeon

2018-07-01

We reexamine a renormalizable model of a fermionic dark matter with a gauge singlet Dirac fermion and a real singlet scalar which can ameliorate the scalar mass hierarchy problem of the Standard Model (SM). Our model setup is the minimal extension of the SM for which a realistic dark matter (DM) candidate is provided and the cancellation of one-loop quadratic divergence to the scalar masses can be achieved by the Veltman condition (VC) simultaneously. This model extension, although renormalizable, can be considered as an effective low-energy theory valid up to cut-off energies about 10 TeV. We calculate the one-loop quadratic divergence contributions of the new scalar and fermionic DM singlets, and constrain the model parameters using the VC and the perturbative unitarity conditions. Taking into account the invisible Higgs decay measurement, we show the allowed region of new physics parameters satisfying the recent measurement of relic abundance. With the obtained parameter set, we predict the elastic scattering cross section of the new singlet fermion into target nuclei for a direct detection of the dark matter. We also perform the full analysis with arbitrary set of parameters without the VC as a comparison, and discuss the implication of the constraints by the VC in detail.

Minimally doubled fermions and spontaneous chiral symmetry breaking

Directory of Open Access Journals (Sweden)

Osmanaj (Zeqirllari Rudina

2018-01-01

Full Text Available Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

Minimally doubled fermions and spontaneous chiral symmetry breaking

Science.gov (United States)

Osmanaj (Zeqirllari), Rudina; Hyka (Xhako), Dafina

2018-03-01

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks - Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss - Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

The Fermion boson interaction within the linear sigma model at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Caldas, H.C.G. [Fundacao de Ensino Superior de Sao Joao del Rei (FUNREI), MG (Brazil). Dept. de Ciencias Naturais (DCNAT)

2000-07-01

We study the interaction of massless bosons at finite temperature. Specifically, we calculate the self-energy of massless fermions due to interaction with massless bosons at high temperature, which is the region where thermal effects are maximal. The calculations are concentrated in the limit of vanishing fermion three momentum and after considering the effective boson dressed mass, we obtain the damping rate of the fermion. It is shown that in the limit k{sub O} <fermion acquire a thermal mass of order gT and the leading term of the fermion damping rate is of order g{sup 2} T + g{sup 3} T. (author)

Reciprocal mass tensor : a general form

International Nuclear Information System (INIS)

Roy, C.L.

1978-01-01

Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)

A new deteriorated energy-momentum tensor

International Nuclear Information System (INIS)

Duff, M.J.

1982-01-01

The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)

Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

(Ln-bar, g)-spaces. Special tensor fields

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces

The Riemann-Lovelock Curvature Tensor

OpenAIRE

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

The Continuum Limit of Causal Fermion Systems

OpenAIRE

Finster, Felix

2016-01-01

This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by...

The Chiral Index of the Fermionic Signature Operator

OpenAIRE

Finster, Felix

2014-01-01

We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators thereon for which our index is non-trivial.

Look-ahead fermion algorithm

International Nuclear Information System (INIS)

Grady, M.

1986-01-01

I describe a fast fermion algorithm which utilizes pseudofermion fields but appears to have little or no systematic error. Test simulations on two-dimensional gauge theories are described. A possible justification for the algorithm being exact is discussed. 8 refs

Superdeformations and fermion dynamical symmetries

International Nuclear Information System (INIS)

Wu, Cheng-Li

1990-01-01

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 SU 3 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 SU 3 fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU 3 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

Landau levels of Majorana fermions in a spin liquid

NARCIS (Netherlands)

Rachel, Stephan; Fritz, Lars; Vojta, Matthias

2016-01-01

Majorana fermions were originally proposed as elementary particles acting as their own antiparticles. In recent years, it has become clear that Majorana fermions can instead be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here

X-ray imaging bilinear staggered GaAs detectors

Energy Technology Data Exchange (ETDEWEB)

Achmadullin, R.A.; Dvoryankin, V.F. E-mail: vfd217@ire216.msk.su; Dvoryankina, G.G.; Dikaev, Y.M.Yu.M.; Krikunov, A.I.; Kudryashov, A.A.; Panova, T.M.; Petrov, A.G.; Telegin, A.A

2004-09-21

The multichannel bilinear X-ray detector based on epitaxial GaAs structures is developed to obtain a digital X-ray image. Each detector operates in photovoltaic mode without reverse bias that enables almost complete elimination of detector noise arising due to leakage currents. The sensitivity range of the epitaxial GaAs photovoltaic X-ray detector covers the effective energies from 8 to 120 keV. A maximum response of the detector operating in the short-circuit mode was observed at an energy of 35 keV and amounted to 30 {mu}A min/(Gy cm{sup 2}). The multichannel detector was made of 1024 pixels with pitch of 0.8 mm. The spatial resolution of double staggered sensor row is twice as high as the resolution of that of single sensor row with the same pitch. Measured spatial resolution is 1.2 line-pairs/mm, contrast sensitivity not worse 1% and dynamic range defined as the ratio of maximum detectable X-ray signal to electronic noise level more than 2000 are received.

X-ray imaging bilinear staggered GaAs detectors

International Nuclear Information System (INIS)

Achmadullin, R.A.; Dvoryankin, V.F.; Dvoryankina, G.G.; Dikaev, Y.M.Yu.M.; Krikunov, A.I.; Kudryashov, A.A.; Panova, T.M.; Petrov, A.G.; Telegin, A.A.

2004-01-01

The multichannel bilinear X-ray detector based on epitaxial GaAs structures is developed to obtain a digital X-ray image. Each detector operates in photovoltaic mode without reverse bias that enables almost complete elimination of detector noise arising due to leakage currents. The sensitivity range of the epitaxial GaAs photovoltaic X-ray detector covers the effective energies from 8 to 120 keV. A maximum response of the detector operating in the short-circuit mode was observed at an energy of 35 keV and amounted to 30 μA min/(Gy cm 2 ). The multichannel detector was made of 1024 pixels with pitch of 0.8 mm. The spatial resolution of double staggered sensor row is twice as high as the resolution of that of single sensor row with the same pitch. Measured spatial resolution is 1.2 line-pairs/mm, contrast sensitivity not worse 1% and dynamic range defined as the ratio of maximum detectable X-ray signal to electronic noise level more than 2000 are received

Symmetries of Ginsparg-Wilson chiral fermions

International Nuclear Information System (INIS)

Mandula, Jeffrey E.

2009-01-01

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

Fidelity Witnesses for Fermionic Quantum Simulations

Science.gov (United States)

Gluza, M.; Kliesch, M.; Eisert, J.; Aolita, L.

2018-05-01

The experimental interest and developments in quantum spin-1 /2 chains has increased uninterruptedly over the past decade. In many instances, the target quantum simulation belongs to the broader class of noninteracting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1 /2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.

Dirac Fermions in an Antiferromagnetic Semimetal

Science.gov (United States)

Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng; Shou-Cheng Zhang's Group Team, Prof.

Analogues of the elementary particles have been extensively searched for in condensed matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low energy excitations in materials now known as Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry  and inversion symmetry "". Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where both  and "" are broken but their combination "" is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points under symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism. We acknowledge the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515, NSF under Grant No.DMR-1305677 and FAME, one of six centers of STARnet.

Causal signal transmission by quantum fields. III: Coherent response of fermions

International Nuclear Information System (INIS)

Plimak, L.I.; Stenholm, S.

2009-01-01

Structural response properties of fermionic fields are investigated. In the presence of fermions the key technical concept becomes response combination, or R-normal product, of field operators. It generalises the notion of time-normal operator product to response problems. Time-normal products are a special case of R-normal products without inputs; this paper thus also generalises the concept of time-normal ordering to fermions. Explicit causality of R-normal products of arbitrary (bosonic and/or fermionic) field operators is proven, and explicit relations expressing them by conventional Green's functions of quantum field theory are derived

Fermion doubling on a lattice and topological aspects of chiral anomaly

International Nuclear Information System (INIS)

Goswami, G.; Bandyopadhyay, P.

1997-01-01

The problem of fermion doubling on a lattice has been discussed here from the specific geometrical properties of a lattice structure and topological aspects of chiral anomaly. It is argued that there cannot be chiral anomaly on a lattice and as such there cannot be any conserved charge. This unveils the root cause of fermion doubling, and the unwanted fermions just reflect the geometrical properties of a lattice and may be viewed as to represent the open-quotes fictitiousclose quotes chiral spinors associated with the lattice structure which make chiral fermions anomaly free. copyright 1997 American Institute of Physics

The Physical Interpretation of the Lanczos Tensor

OpenAIRE

Roberts, Mark D.

1999-01-01

The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...

Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

Science.gov (United States)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

3D reconstruction of tensors and vectors

International Nuclear Information System (INIS)

Defrise, Michel; Gullberg, Grant T.

2005-01-01

Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields

A Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies

Science.gov (United States)

Lu, Wei

2017-09-01

We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu-Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.

On the restoration of symmetry in paired Fermion systems

International Nuclear Information System (INIS)

Flocard, H.

1997-01-01

We consider the problem of symmetry restoration as treated by the method of variation after projection (VAP) on good quantum numbers. We show that for compact groups, the convergence of the connected-linked expansion of the VAP kernels over the physically relevant interval of integration of the pairing gauge angle is not guaranteed. We propose instead a method which generates approximations of increasing precision which are periodic with respect to the gauge angle while differing from truncations of the Fourier expansion of the VAP kernels. For the projection on good particle number in paired fermion systems, this new approach is shown to be equivalent to an expansion in powers of the pairing tensor. For the lowest order approximation, an analytical integration over the gauge angle is performed explicitly. It provides the algebraic forms of the single particle Hamiltonian and of the pairing field entering generalized Hartree endash Fock endash Bogoljubov equations. Contrary to most approximations, the validity of the expressions for the energy and mean values of operators thus obtained is not a priori restricted where the fluctuation of the operator associated with the broken symmetry is large. We also derive the first-order correction to the pairing-order parameter. We test the quality of the proposed method on a non-trivial soluble model. copyright 1997 Academic Press, Inc

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

Science.gov (United States)

Liu, Chunlei; Murphy, Nicole E.; Li, Wei

2012-01-01

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987

Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow

Science.gov (United States)

Alam, Meheboob; Saha, Saikat

2014-11-01

The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.