Anomalies for a nonlinear transformation

We have investigated anomalies associated with a nonlinear transformation, and found that even a simple kind of nonlinear transformation gives rise to many anomalies. The nonlinear transformation adopted in this paper provides an anomalous operator identity relation for a four-fermion operator. It resembles closely the Ward-Takahashi identity for the Chiral transformation given in the configuration space. The comparison of these two relations suggests how to regulate singularities in the Ward-Takahashi identity. In due course, we also encounter a novel anomaly, which is separate from the dilatation and chiral anomalies.     

A quantum field theory of lattice dynamics at finite temperature

A quantum field theoretical treatment of three-dimensional cubic crystals at finite temperature is presented from the view-point of the spontaneous breakdown of the spatial translational invariance using thermo field theory. The effective interaction Hamiltonian is constructed by taking into account the dynamical map of the molecular density operator which is obtained from the Ward-Takahashi relations. The acoustic phonons are expected to be the excitation of particle-hole pairs. The conventional secular equation for the lattice vibrations is obtained by neglecting some quantum effects in the Bethe-Salpeter equation for the molecular density fluctuations. The phonon spectra, the phonon propagators and the dynamical map of the molecular density operator are calculated at finite temperature.     

Goldstone realization of Lorentz-symmetry and supersymmetry at finite temperature

The Ward-Takahashi identities of Lorentz symmetry are examined at finite temperature. It is shown that the Lorentz symmetry is broken with the Goldstone realization. The analogy with finite-temperature supersymmetry-breaking in an R-invariant model is explained.     

A quantum field theory of lattice dynamics and melting in fcc crystals

Phonons in crystals are constructed by particle-hole excitations of ion cores. The Ward-Takahashi relations play an essential role in constructing the lattice dynamics and determining the melting temperature. The phonon dispersion and the melting temperature in fcc crystals are presented. In principle, our theory covers metallic, covalent and molecular crystals.     

Renormalized Ward-Takahashi relations and topological susceptibility with staggered fermions

Local (axial) vector currents and (pseudo) scalar fields are constructed, renormalized and used to derive Ward-Takahashi relations for staggered fermions in lattice QCD. With the help of these a lattice derivation is given of the Witten-Veneziano formula for the flavor singlet pseudoscalar particle. We discuss how the ensuing topological susceptibility is to be evaluated and argue that it is finite.     

Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian

Based on the phase-space generating functional of a system with a singular Lagrangion,the Ward identities under global transformation in phase are deduced.The quantum conservation laws under the global symmetry transiormation are also derived which is in general different from classical Hoether's ones.The preliminary application of our formulation to the Yang-Mills theory the Ward-Takahashi identity and BRS conserved quantity for BRS transformation are presented.Applying to non-Abelian-Chern-Simons theory the quantum conserved angular momentum (QCAM) are obtained.The QCAM differs form classical one because the former needs to take into account the distribution of angular momentum of ghost innon-Abelian-Chern-Simons theory.     

Massless QCD and chiral symmetry breaking

It is well known that chiral symmetry is spontaneously broken in QCD. To relate this fact to non-perturbative features of the theory, like instantons, we start with a massless lagrangian and perform a non-linear chiral colored singlet transformation on the quark fields which yields (by means of Fujikawa's method) essentially two terms in the lagrangian. First a quark mass term induced by instantons and secondly a coupling between pseudoscalar mesons and the axial anomaly. Ward-Takahashi identities can be derived. To clarify the presence of this induced mass term we calculate its first perturbative part up to the two-loop level.     

Vertex Correction at Finite Temperature and Decoupling Transition in (2+1) Dimensional Chiral Gross-Neveu Model

With the aid of imaginary time temperature field theory and fermion mass spectrum derived from Ward-Takahashi identities with composite fields,the vertex correction among fermions and σ meson is calculated beyond the leading order in 1/N expansion,and the change of vertex function with temperature and decoupling transition are discussed in (2+1) dimensional chiral Gross-Neveu model.It turns out that the critical temperature of decoupling transitionarises with increasing fermion mass and π meson mass at zero temperature;the vertex correction resulting from thermal fluctuation will affect the fermion dynamical mass and cannot be ignored at finite temperature.     

Finite-temperature supersymmetry: the Wess-Zumino model

We investigate the breakdown of supersymmetry at finite temperature. While it has been proven that temperature always breaks supersymmetry, the nature of this breaking is less clear. On the one hand, a study of the Ward-Takahashi identities suggests a spontaneous breakdown of supersymmetry without the existence of a Goldstino, while on the other hand it has been shown that in any supersymmetric plasma there should exist a massless fermionic collective excitation, the phonino. Aim of this work is to unify these two approaches. For the Wess-Zumino model, it is shown that the phonino exists and contributes to the supersymmetric Ward-Takahashi identities in the right way displaying that supersymmetry is broken spontaneously with the phonino as the Goldstone fermion.     

Fluctuations in nonequilibrium systems and broken supersymmetry

The fluctuation-dissipation theorem is not expected to hold for systems that either violate detailed balance or have time-dependent or nonpotential forces. Therefore the relation between response and correlation functions should have contributions due to the nonequilibrium nature. An explicit formula for such a contribution is calculated, which in the present derivation appears as a historydependent term. These relations are the Ward-Takahashi identities of a supersymmetric formulation of the Langevin models, and the new term results from a broken supersymmetry.     

Ward-takahashi identities and Noether’s theorem in quantum field theory

The gap in the mathematical derivation of Noether’s theorem, and also of the Ward-Takahashi identities, caused by performing variation before quantization is closed by introduction of variational calculus for operator fields. It is demonstrated that both Noether’s theorem and the Ward-Takahashi identities retain full validity in quantum field theory.     

广义QCD中正则形式的Ward恒等式

导出了高阶微商奇异拉氏量系统正则形式的Ward恒等式并将其应用于广义色动力学(QCD),得到了广义QCD中规范场和鬼场正规顶角间的某些新关系,它们有别于BRS不变性所导致的结果;还得到了广义QCD中的PCAC和AVV顶角的Ward恒等式.     

Critical behavior of a spherical model with a free surface

Critical phenomena ind-dimensional ferromagnetic spherical models on hypercubic lattices with free surfaces are studied. The surface specific heat and surface susceptibilities are obtained. The exponents characterizing the divergence of these surface quantities at the bulk critical temperature are found to satisfy recently proposed scaling relations. The variation of the susceptibility with distance from the surface is also discussed. The author's recent scaling theory for surface properties is investigated in detail, and found to give an exact representation for the free energy of a three-dimensional spherical model of finite thickness in finite bulk and surface magnetic fields. A scaling form for the surface free energy is derived.     

Derivation of the Ward--Takahashi Identity in GWS Gauge Theory

With the help of a postulate of gauge group parameter involved with ghost fields, the infinitesimal gauge transformation laws preserving the gauge-invariance of the quantum Lagrangian itself of the quantized Glashow- Weinberg-Salam model are established precisely. The corresponding Ward-Takahashi identity for the model is derived exactly.     

Chiral and conformal anomalies in lattice gauge theory

The continuum limit of the chiral and conformal (Weyl) Ward-Takahashi identities in the lattice Wilson action is studied. The Wilson term works for the chiral anomaly, but it gives rise to-15 times the conventional conformal anomaly for a smallr-parameter and a very sensitiver-dependence of the Λ-parameter. This shows that the strong symmetry breaking by the Wilson term by itself does not necessarily generate correct anomalies. In the lattice regularization the functional Jacobian factors becomec-numbers and do not contribute to anomalies, corresponding to the cut-off of short distance components; the naive continuum limit of lattice WT identities can thus behave differently from continuum ones. To reconstruct conventional identities from lattice relations, the lattice composite operators should be rewritten in terms of relevant continuum operators. In general, this identification of relevant operators is facilitated either by the procedure corresponding to Zimmermann's normal product algorithm or simply by the use of auxiliary regulators such as the dimensional regulator.     

Electrodynamics of Superconductors as a Consequence of Local Gauge Invariance

The electromagnetic properties of superconductors are studied in the framework of a quantum gauge-invariant theory. The formulation is developed in the generalized pair approximation which preserves the Ward-Takahashi identities. The macroscopic equations which regulate current and electromagnetic fields are derived by means of the boson transformation method. Comparison with previous works is reported.     

Supersymmetric field theories at finite temperature

We show by explicit calculations to second and third order in perturbation theory, that finite temperature effects do not break the supersymmetry Ward-Takahashi identities for graded thermal Green functions of the Wess-Zumino model. Moreover, it is argued that this result is true to all orders in perturbation theory, and further, true for a wide class of supersymmetric theories. We point out, however, that these identities can be broken in the course of a phase transition that restores an originally broken internal symmetry.     

Transformation properties of proper vertices in gauge theories

The Ward-Takahashi identities for (single-particle irreducible) proper vertices are derived for non-Abelian gauge theories; the renormalization of such theories, previously discussed in terms of the Ward-Takahashi identities for Green functions, can now be considerably simplified.     

Dynamic modeling of beams with non-material,deformation-dependent boundary conditions

In conventional problems of structural mechanics, both kinematic boundary conditions and external forces are prescribed at fixed material points that are known in advance. If, however, a structure may move relative to its supports, the position of the imposed constraint relations generally changes in the course of motion. A class of problems which inherently exhibits this particular type of non-material boundary conditions is that of axially moving continua. Despite varying in time, the positions of the supports relative to the material points of the body have usually assumed to be known a priori throughout the deformation process in previous investigations. This requirement is abandoned in the present paper, where the dynamic behavior of a structure is studied, which may move freely relative to one of its supports. As a consequence, the position of such a non-material boundary relative to the structure does not only change in time but also depends on the current state of deformation of the body. The variational formulation of the equilibrium relations of a slender beam that may undergo large deformations is presented. To this end, a theory based on Reissner's geometrically exact relations for the plane deformation of beams is adopted, in which shear deformation is neglected for the sake of brevity. Before a finite element scheme is developed, a deformation-dependent transformation of the beam's material coordinate is introduced, by which the varying positions of the constraint relations are mapped onto fixed points with respect to the new non-material coordinate. By means of this transformation, additional convective terms emerge from the virtual work of the inertia forces, whose symmetry properties turn out to be different from what has previously been presented in the literature. In order to obtain approximate solutions, a finite element discretization utilizing absolute nodal displacements as coordinates is subsequently used in characteristic numerical examples, which give an insight into the complex dynamic behavior of problems of this type. On the one hand, the free vibrations of a statically pre-deformed beam are investigated, on the other hand, an extended version of the sliding beam problem is studied.     

Fermion-Boson Vertex at Finite Chemical Potential

Based on the Ward-Takahashi identity at finite chemical potential and Lorentz structure analyms, we generalize the Ball-Chiu vertex to the case of nonzero chemical potential and obtain the general form of the frmionboson vertex in QED at finite chemical potential.