Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD （Quantum Chromodynamics） leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of the vertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion. It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.     

Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion.It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.     

Gauge Transformation for BCr-KP Hierarchy and Its Compatibility with Additional Symmetry

The BCr-KP hierarchy is an important sub-hierarchy of the KP hierarchy. In this paper, the BCr-KP hierarchy is investigated from three aspects. Firstly, we study the gauge transformation for the BCr-KP hierarchy.Different from the KP hierarchy, the gauge transformation must keep the constraint of the BCr-KP hierarchy. Secondly,we study the gauge transformation for the constrained BCr-KP hierarchy. In this case, the constraints of the Lax operator must be invariant under the gauge transformation. At last, the compatibility between the additional symmetry and the gauge transformation for the BCr-KP hierarchy is explored.     

Relativistic Linear Spacetime Transformations Based on Symmetry

Usually the Lorentz transformations are derived from the conservation of the spacetime interval. We propose here a way of obtaining spacetime transformations between two inertial frames directly from symmetry, the isotropy of the space and principle of relativity. The transformation is uniquely defined except for a constant e, that depends only on the process of synchronization of clocks inside each system. Relativistic velocity addition is obtained, and it is shown that the set of velocities is a bounded symmetric domain. If e=0, Galilean transformations are obtained. If e>0, the speed 1/e and a spacetime interval are conserved. By assuming constancy of the speed of light, we get e=1/c ² and the transformation between the frames becomes the Lorentz transformation. If e<0, a proper speed and a Hilbertian norm are conserved.     

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock–Schwinger (FS) gauge for the Abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev–Popov ghosts-free non-Abelian gauge theories. This method is expected to be applicable to non-Abelian gauge theories including supersymmetric ones.     

A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A generalized Yang-Mills model, which contains, besides the vector part V_μ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A maximally generalized Yang-Mills model, which contains, besides the vector part V_μ, also an axial-vector part A_μ, a scalar part S, a pseudoscalar part P, and a tensor part T_μν, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

Transverse Ward—Takahshi Relation for the Vector Vertex in Quantum Field Theory

The transverse Ward-Takahashi(W-T) realtion for the Vector vertex in quantum filed theory is derived by calculation the coul of the time-ordered product of the three-point function inclduing the vector current operator.This provides the constraint on the transverse part of the vertex.By combining the transverse and normal (longitudinal)W-T identities,we obtain the expression for the full vector vertex function.     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.``     

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T²)_local algebra and the generalized Kac-Moody algebra \hat g(T²). In this paper, we construct the linearly realized gauge theory of the SDIFF(T²)_local-generalized Kac-Moody \hat G(T²) symmetry.     

Fermion Self-Energy and Chiral Symmetry Breaking from Four-Fermion and Gauge Interactions

The exact analytic solutions of the linearized Schwinger-Dyson equation of fermion self-energy are used to obtain the effective four-fermion and gauge coupling criticality curves for dynamical chiral symmetry breaking. The results show that when the zero-momentum gauge coupling a(0) < a₀(0), the critical gauge coupling in the pure gauge interaction case, the minimal critical four-fermion coupling β_min is always nonzero and positive and will go up as the a(0) decreases. The use of the exact solutions also allows us to make quite definite estimations of the momentum scales where chiral symmetry breaking would happen if the values of an infrared parameter ξ are given separately.     

定域内对称和规范场--为杨-米尔斯场五十周年而作

文章为杨-米尔斯的历史性论文发表50年而写，扼要阐述非阿贝尔规范场理论这篇原创论文的主要思想和它的巨大影响。     

正则Ward恒等式和Abel规范理论中动力学质量的产生

文中基于约束Hamilton系统理论用Faddeev-Senjanovic路径积分量子化方法,重新讨论了Cornwall-Norton和Jackiw-Johnson模型的量子化,导出了这两个系统的正则Ward恒等式,利用导出的正则Ward恒等式,得到了包括费米子和束缚态的质量谱.所得的结果与其他方法导出的结果相同     

The Effects of Solution Transformations to the System with Color Parameters

The effects of solution transformations to the six-and eight-vertex systems are discussed.There are four Kinds of effects,the Hamiltonian of the system is invariant,Its coupling coefficients change,some additional terms appear in the Hamiltonian,and the spin of the system is rotated by some angle about z axis under these transformations.In all the cases,the systems are still integrable if they are so before the transformation.     

Darboux Transformations and Symmetries of a(2+1)-Extension of Burgers Equation

We first derive a Darboux transformation for a (2+ 1)-extension of Burgers equation. Then we consider theLie symmetries, symmetry algebra, and symmetry reductions of the equation, and use symmetry reductions to obtaingroup-invariant solutions to the equation.     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the reoativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

Unitary and Antiunitary Operators Mapping Vectors to Parallel or to Orthogonal Ones, with Applications to Symmetry Transformations

Unitary and antiunitary operators which map vectors either to parallel or to orthogonal vectors are characterized. As an application the results are used to show that symmetry transformations induced by real functions are identity transformations.