Showing papers on "Explicit symmetry breaking published in 1993"
Book•
01 Jan 1993
TL;DR: In this paper, a deep connection between dynamical symmetry breaking in condensed matter physics and particle physics is emphasized, and applications of DSB to such realistic theories as chromo-dynamics and electroweak interactions are also considered Problems intimately connected with DSB (anomalies, effective lagrangian approach) are also discussed.
Abstract: In this text, differential aspects of dynamical symmetry breaking (DSB) in quantum field theory are discussed in detail A deep connection between this phenomenon in condensed matter physics and particle physics is emphasized Applications of DSB to such realistic theories as chromo-dynamics and electroweak interactions are also considered Problems intimately connected with DSB (anomalies, effective lagrangian approach) are also discussed
369 citations
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340 citations
TL;DR: The Continuous Symmetry Measure (CSM) as mentioned in this paper is a continuous property measure that measures the symmetry of tetrahedral tetrahedra in two and three dimensions. And it can be used to evaluate the symmetry properties of tetric structures.
Abstract: We treat symmetry as a continuous property rather than a discrete "yes or no" one. Here we generalize the approach developed for symmetry elements (Part 1: J. Am. Chem. SOC. 1992,114,7843-7851) to any symmetry group in two and three dimensions. Using the Continuous Symmetry Measure (CSM) method, it is possible to evaluate quantitatively how much of any symmetry exists in a nonsymmetric configuration; what is the nearest symmetry group of any given configuration; and how the symmetrized shapes, with respect to any symmetry group, look. The CSM approach is first presented in a practical easy-to-implement set of rules, which are later proven in a rigorous mathematical layout. Most of our examples concentrate on tetrahedral structures because of their key importance in chemistry. Thus, we show how to evaluate the amount of tetrahedricity (Td) existing in nonsymmetric tetrahedra; the amount of other symmetries they contain; and the continuous symmetry changes in fluctuating, vibrating, and rotating tetrahedra. The tool we developed bears on any physical or chemical process and property which is either governed by symmetry considerations or which is describable in terms of changes in symmetry.
187 citations
TL;DR: In this article, the authors derived a geometric action for the tensionless tensile string and discussed its symmetries and field equations, and showed that the Weyl symmetry of the usual string is replaced by a global space-time conformal symmetry in the $T to 0$ limit.
Abstract: {}From the ordinary tensile string we derive a geometric action for the tensionless ($T=0$) string and discuss its symmetries and field equations. The Weyl symmetry of the usual string is shown to be replaced by a global space-time conformal symmetry in the $T\to 0$ limit. We present the explicit expressions for the generators of this group in the light-cone gauge. Using these, we quantize the theory in an operator form and require the conformal symmetry to remain a symmetry of the quantum theory. Modulo details concerning zero-modes that are discussed in the paper, this leads to the stringent restriction that the physical states should be singlets under space-time diffeomorphisms, hinting at a topological theory. We present the details of the calculation that leads to this conclusion.
133 citations
TL;DR: In this paper, it was shown that for axisymmetric spacetimes with a conformal symmetry, the axial Killing vector and the conformal Killing vector must commute.
Abstract: Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, the authors prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others must vanish or else the symmetry is larger than that originally considered. The results are completely general, and do not depend on Einstein's equations or any particular matter content.
108 citations
TL;DR: In this article, the authors considered the case of uniaxial vortex glass in which the vortices are free to move only in one direction, and showed that a phase transition takes place between the phase in which random potential is irrelevant, to the phase with one-step replica symmetry breaking.
Abstract: Destruction of the long-range order in a vortex crystal by a random potential is expected to be accompanied by the formation of a glasslike phase--the so-called vortex glass. The properties of such a phase are investigated in the framework of the self-consistent harmonic approximation, taking into account the possibility of replica symmetry breaking. The main attention is given to the problem of the uniaxial vortex glass in which the vortices are free to move only in one direction. We obtain the result that in the two-dimensional case, upon lowering the temperature, a phase transition takes place between the phase in which the random potential is irrelevant, to the phase with one-step replica symmetry breaking. For 2D4 the random potential is always relevant and the replica symmetry breaking is of the hierarchical type. In both cases, the fluctuations of the displacement in the glassy phase diverge logarithmically. The same conclusions are shown to be valid for the case of a biaxial vortex glass in the absence of dislocations. The results obtained are also applicable to the description of the pinning of charge density waves.
74 citations
TL;DR: In this article, the modern point of view on the physics of the spin-glass state is considered, and the physical meaning of the phenomenon known as replica symmetry breaking is discussed.
Abstract: The modern point of view on the physics of the spin-glass state is considered. The physical meaning of the phenomenon known as the replica symmetry breaking is discussed.
71 citations
TL;DR: In this paper, the subject of quantum mechanical symmetry breaking is addressed using only basic quantum mechanics, and several examples from different areas of physics are examined, such as physics, astronomy, and astronomy.
Abstract: The subject of anomalies, i.e., quantum mechanical symmetry breaking, is addressed using only basic quantum mechanics. Examples from different areas of physics are examined.
59 citations
TL;DR: This paper introduces the concept of “index” of an element as part of the whole structure, which is the number, of its distinct symmetrical images, and introduces the rule for assembly to perform as usual, but to count each element as many times as its index.
Abstract: Symmetry, and related questions of group theory, especially representation theory, are well-known, popular topics among physicists. This paper describes how these classical ideas can be put to use in the realm of finite element computations by substituting a family of independent problems on a reduced domain (the “symmetry cell”) for the original problem on the whole domain. Two specific difficulties appear : one is how to set boundary conditions on symmetry planes (representation theory gives the answer); the other is how to proceed with the assembly of finite elements that constitute the symmetry cell. To deal with this, this paper introduces the concept of “index” of an element as part of the whole structure, which is the number, of its distinct symmetrical images. The rule for assembly then becomes to perform as usual, but to count each element as many times as its index.
47 citations
TL;DR: In this paper, the spectral statistics of independent electrons moving at zero temperature in a weakly disordered metallic ring threaded by a magnetic flux were analyzed based on the supersymmetry method involving both commuting and anticommuting variables.
Abstract: The authors consider the spectral statistics of independent electrons moving at zero temperature in a weakly disordered metallic ring threaded by a magnetic flux. The analysis is based on the supersymmetry method involving both commuting and anticommuting variables. Besides, they consider an ensemble of Gaussian distributed symmetric random matrices (Gaussian orthogonal ensemble) which are perturbed by a small time reversal symmetry breaking contribution. For energies smaller than the inverse diffusion time around the ring Ec, the spectral correlation functions of both models can be represented in terms of supermatrix integrals of identical structure. In conformity with recent numerical results, this implies that the spectral properties of the two models coincide. These matrix integrals are to a large extent universal, i.e. they depend only on two physical parameters: the mean level spacing and a symmetry breaking parameter which is identified as the typical sensitivity of levels to the time reversal symmetry breaking perturbation. The authors parametrize the relevant matrix coset space of the nonlinear sigma -model in a novel way which is particularly convenient for treating models in the crossover between the two symmetry classes. As an example, they present a detailed calculation of the level-level correlation function. The basic formalism, however, applies quite generally and can be used for the investigation of different types of correlation functions and system geometries as well.
45 citations
Book•
15 Oct 1993
TL;DR: A review of matrix algebra and quantum mechanics can be found in this paper, where the authors present a theory and application of symmetry representation products for Semiclassical and Quantum Mechanics: Dynamics with High Quanta.
Abstract: A Review of Matrix Algebra and Quantum Mechanics. Basic Theory and Applications of Symmetry Representations (Abelian Symmetry Groups). Basic Theory and Applications of Symmetry Representations (Non-Abelian Symmetry Groups). Theory and Applications of Higher Finite Symmetry and Induced Representations. Representations of Continuous Rotation Groups and Applications. Theory and Applications of Symmetry Representation Products (Finite Groups). Theory and Application of Symmetry Representation Products (Continuous Rotation Groups). Symmetry Analysis for Semiclassical and Quantum Mechanics: Dynamics with High Quanta. Appendices. Index.
TL;DR: In this paper, the authors extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other, and show that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies symmetry breaking.
Abstract: We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.
TL;DR: In this article, a simple zero-dimensional model of a disordered system is studied by means of a variational principle for the replicated partition function, and the replica symmetric ansatz for the solution of the variational equations gives correct results down to zero temperature if the hamiltonian possesses typically one minimum only.
TL;DR: The problem of spontaneous symmetry breaking in scalar field theories quantized on the light cone is considered and the consistency of the formalism is checked in an explicit perturbative calculation in (1+1)-dimensional ${\ensuremath{\varphi}}^{4}$ theory.
Abstract: The problem of spontaneous symmetry breaking in scalar field theories quantized on the light cone is considered. Within the framework of "discretized" light-cone field theory, a constrained zero mode of the scalar field, which is necessary for obtaining a consistent dynamics, is responsible for supporting nonzero vacuum expectation values classically. This basic structure is shown to carry over to the quantum theory as well, and the consistency of the formalism is checked in an explicit perturbative calculation in (1+1)-dimensional ${\ensuremath{\varphi}}^{4}$ theory.
TL;DR: Comparison with recent numerical results for the S=1/2 case gives strong support for the existence of long range order in this quantum antiferromagnets system.
Abstract: We show that the spontaneous symmetry breaking mechanism in quantum antiferromagnets is due to the collapse, in the thermodynamical limit, of an infinite set of excited states onto the ground state. We characterize both the nature and the scaling of the relevant tower of states for the quantum antiferromagnet on the triangular lattice. Comparison with recent numerical results for the S=1/2 case gives strong support for the existence of long range order in this system
TL;DR: In this article, the authors studied symmetry breaking in Z2 symmetric large N matrix models and showed that there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients Rn and Sn that all lead to identical free energies and eigenvalue densities.
TL;DR: The current study investigated the different effects of axial reflective versus rotational symmetry and found that systematic errors were structured by the underlying approximate symmetries, and the problem of quantifying symmetry.
Abstract: Bingham and Muchisky (1993) found that observers were very accurate in determining the location of the center of mass in planar objects. Systematic errors were affected primarily by object orientation, while random errors varied with the amount of symmetry. Radial and axial reflective symmetry affected errors in different ways. In the current study, we investigated the different effects of axial reflective versus rotational symmetry. All random errors decreased with increasing rotational symmetry. Axial reflective symmetry further reduced errors in the direction perpendicular to the axis. We replicated the effect on systematic error of orientation. However, we also found an effect of the perturbation of symmetry that suggested that observers used an approximation to symmetry. To investigate this possibility, we constructed a series of objects in which axial reflective symmetry was established and then perturbed by varying amounts. We found that systematic errors were structured by the underlying approximate symmetries, and we discuss the problem of quantifying symmetry.
TL;DR: It is shown that partial dynamical symmetry may cause suppression of chaos even in cases where the fraction of states which has the symmetry vanishes in the classical limit.
Abstract: Partial dynamical symmetry is a situation in which the Hamiltonian does not have a certain symmetry yet a subset of its eigenstates does. It is shown that partial dynamical symmetry may cause suppression of chaos even in cases where the fraction of states which has the symmetry vanishes in the classical limit. The average entropy associated with the symmetry is a sensitive quantum measure of the partial symmetry and its effect on the chaotic dynamics.
TL;DR: The character of the first-order Stark effect in the energy levels of real symmetric top is examined in this paper, where the terms responsible for the breaking of the nominal degeneracy of levels with fK units of angular momentum around the symmetry axis are derived from off-diagonal higher-order distortion coupling (for ro-vibronic states of non-degenerate symmetry) and from spin-rotation and spin-spin interactions.
Abstract: The character of the first-order Stark effect in the energy levels of real symmetric tops is examined. Group theory shows that the only allowed levels are nondegenerate, and as a result time reversal symmetry requires that such eigenstates not have a nonzero orientation required for a permanent electric dipole moment and thus a first-order Stark effect. The terms responsible for the breaking of the nominal degeneracy of levels with fK units of angular momentum around the symmetry axis are shown to derive from off-diagonal higher-order distortion coupling (for ro-vibronic states of nondegenerate symmetry) and from spin-rotation and spin-spin interactions (for degenerate ro-vibronic states). A semiclassical model demonstrates that both effects can be viewed as caused by tunneling and as such decrease rapidly for increasing K. For a C3 symmetry symmetric top, the resulting splittings are a few kilohertz for K = 1 but only on the order of 10-4 Hz for K = 2.
TL;DR: The symmetry of the superconducting-phase condensate of Bi2Sr2CaCu2Ox with photoemission at high energy and angular resolution unambiguously demonstrates that the photohole must include non-s-wave components.
Abstract: We analyzed the symmetry of the superconducting-phase condensate of Bi2Sr2CaCu2Ox with photoemission at high energy and angular resolution. The result unambiguously demonstrates that the photohole must include non-s-wave components. Under the hypothesis of a pure d-wave symmetry, this would be identified as d(xz) + d(yz). Our superconducting state data are, specifically, incompatible with pure d(x2-y2) symmetry. Mixed symmetries, however, cannot be excluded as long as they include a non-s-wave component. We specifically observe a change in the symmetry of electronic states between the normal state and the superconducting state.
TL;DR: In this paper, the structure of models with effective many-fermion interaction and a finite cutoff in the symmetry-breaking regime is described, and the large-Nc tadpole mechanism for the DSB and the fine-tuning condition in providing the scale invariance are used to classify the set of quasilocal vertices relevant for the dynamic mass formation.
Abstract: We describe the structure of models with effective many-fermion interaction and a finite cutoff in the symmetry-breaking regime. The large-Nc tadpole mechanism for the DSB and the fine-tuning condition in providing the scale invariance are used to classify the set of quasilocal vertices relevant for the dynamic mass formation. It is found that in such effective models the vertices with four, six and eight fermions only should be retained in four-dimensional space.
TL;DR: The phason mode represents the sliding, or what is equivalent, the slow rotation of the double twisted helicoidal modulation wave, restoring the symmetry, lost at the Sm-A- Sm-CA' transition, of the high temperature phase.
Abstract: The dynamics of liquid crystals is in certain respects richer than the dynamics of 3D periodic solids. In con trast to these systems, many liquid crystalline phases ex hibit a continuous rotational symmetry, which can be broken at the transition to phases of lower symmetry. This should allow for the existence of symmetry recover ing, zero frequency Goldstone modes, which are known to occur in particle physics and incommensurate systems. A particularly interesting Goldstone model, which is the subject of this study, should exist in antiferroelectric liquid crystals. of the high temperature phase. In the antiferroelectric Sm-CA' phase, the phason mode represents the sliding, or what is equivalent, the slow rotation of the double twisted helicoidal modulation wave, restoring the symmetry, lost at the Sm-A- Sm-CA' transition. Since the Sm-A * phase has the continuous Dco symmetry, whereas the symmetry of the Sm-CA' phase is discrete, the symmetry recovering phason is here predicted to be a truly gapless Goldstone mode.
TL;DR: In this article, the meson mixing matrix elements usually considered responsible for the bulk of the observed few-body charge symmetry breaking are naturally q 2 -dependent in QCD, and the leading q 2 dependence can be explicitly calculated using chiral perturbation theory to one loop.
TL;DR: In this article, the projected propagator and energy dependent Green's function associated with a given irreducible representation of the symmetry group are derived from the trace formulae analogous to the usual trace formula, that determine the energy levels in a given symmetry class in terms of classical orbits.
Abstract: The author discusses semiclassical approximations that are adapted to given symmetry classes in quantum mechanics. Arbitrary abelian symmetries and also rotational symmetry are treated. Semiclassical approximations are derived for the projected propagator and energy dependent Green's function associated with a given irreducible representation of the symmetry group. From these they derive trace formulae, analogous to the usual trace formula, that determine the energy levels in a given symmetry class in terms of classical orbits.
TL;DR: In this article, the generalized Hartree-Fock method was used to break the chiral symmetry in massless QCD by the use of low energy quark mass in the zero momentum limit.
Abstract: We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.
TL;DR: In this paper, it was shown that for some processes and in a preasymptotic region which may roughly include charmonium and bottomonium, the use of the spin-symmetry may be useful in conjunction with chiral symmetry for light hadrons (soft exchange approximation regime, SEA).
TL;DR: In this paper, the coupling of topological matter to topological Yang-Mills theory in four dimensions is considered and a model is presented and it is shown that, contrary to the two-dimensional case, this coupling may lead to a breaking of the topological symmetry.
TL;DR: In this article, the main building blocks of spontaneous symmetry breaking mechanism in atomic nuclei are discussed and illuminated by examples taken from atomic and nuclear physics, as well as examples from the physics literature.
Abstract: Why can certain nuclei be described in terms of intrinsic shapes with non-spherical, triaxial, or reflection-asymmetric static moments? At first glance a violation of very fundamental symmetries such as rotational invariance, space inversion, or particle number symmetry is astonishing since strong interactions do actually conserve angular momentum, parity, and baryon number. The main building blocks of the spontaneous symmetry breaking mechanism in atomic nuclei are discussed and illuminated by examples taken from atomic and nuclear physics.
TL;DR: The behavior of transfer and return maps in the intermediate region of Chua's circuit and related systems undergoes a number of changes as the symmetry of the dynamics is broken, i.e., the separating planes are moved away from symmetric positions as discussed by the authors.
Abstract: The behavior of transfer and return maps in the intermediate region of Chua's circuit and related systems undergoes a number of changes as the symmetry of the dynamics is broken, i.e., the separating planes are moved away from symmetric positions. We employ the technique of maps induced by the flow of the system and construct the critical curves for the maps in the intermediate region of state space. The influence of a broken symmetry on the critical curves and the flow is discussed in depth. We demonstrate that any breaking of symmetry potentially weakens and eventually destroys the chaos producing mechanisms.
TL;DR: In this paper, the authors provide examples of nonlinear solutions with a variety of different spatio-temporal symmetries, which can be classified by establishing an appropriate group structure.
Abstract: In the presence of a magnetic field, convection may set in at a stationary or an oscillatory bifurcation, giving rise to branches of steady, standing wave and travelling wave solutions. Numerical experiments provide examples of nonlinear solutions with a variety of different spatiotemporal symmetries, which can be classified by establishing an appropriate group structure. For the idealized problem of two-dimensional convection in a stratified layer the system has left-right spatial symmetry and a continuous symmetry with respect to translations in time. For solutions of period P the latter can be reduced to Z 2 symmetry by sampling solutions at intervals of ½P. Then the fundamental steady solution has the spatiotemporal symmetry D 2 = Z 2 ⊗ Z 2 and symmetry-breaking yields solutions with Z 2 symmetry corresponding to travelling waves, standing waves and pulsating waves. A further loss of symmetry leads to modulated waves. Interactions between the fundamental and its first harmonic are described b...