Non-abelian traveling wave solutions for massless QCD2

The field equations for quantum chromodynamics in 1 + 1 dimensions (QCD₂) with massless fermions are shown to admit classical non-abelian traveling wave solutions. In this case, the field equations reduce to the linear Frenet-Serret equations for a curve in the three-space corresponding to an SU(2) subalgebra of the SU(N) gauge group.     

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential Â_i, and find that it has inner structure, namely, Â_i can be decomposed in two parts, hat{b}_i and â_i, where hat{b}_i satisfies gauge transformations while â_i satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U(1) gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor     

Non-abelian gauge structure in neutrino mixing

We discuss the existence of a non-abelian gauge structure associated with flavor mixing. In the specific case of two flavor mixing of Dirac neutrino fields, we show that this reformulation allows to define flavor neutrino states which preserve the Poincaré structure. Phenomenological consequences of our analysis are explored.     

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。     

Gravitational Gauge Interactions of Dirac Field

Gravitational interactions of Dirac field are studied in this paper. Based on gauge principle, quantum gauge theory of gravity, which is perturbatively renormalizable, is formulated in the Minkowski space-time. In quantum gauge theory of gravity, gravity is treated as a kind of fundamental interactions, which is transmitted by gravitational gauge field, and Dirac field couples to gravitational field through gravitational gauge covariant derivative. Based on this theory, we can easily explain gravitational phase effect, which has already been detected by COW experiment.     

Non-abelian T-duality,Ramond fields and coset geometries

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D, D + n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D, D + n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D, D + n) covariant fashion, in analogy to similar constructions in gauged supergravities.

     

The Influence of Quantum Field Fluctuations on Chaotic Dynamics of Yang–Mills System

Abstract

On example of the model field system we demonstrate that quantum fluctuations of non-abelian gauge fields leading to radiative corrections to Higgs potential and spontaneous symmetry breaking can generate order region in phase space of inherently chaotic classical field system. We demonstrate on the example of another model field system that quantum fluctuations do not influence on the chaotic dynamics of non-abelian Yang–Mills fields if the ratio of bare coupling constants of Yang–Mills and Higgs fields is larger then some critical value. This critical value is estimated.     

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.     

Nonrelativistic Wave Equations with Gauge Fields

We illustrate a metric formulation of Galilean invariance by constructing wave equations with gauge fields. It consists of expressing nonrelativistic equations in a covariant form, but with a five-dimensional Riemannian manifold. First we use the tensorial expressions of electromagnetism to obtain the two Galilean limits of electromagnetism found previously by Le Bellac and Lévy-Leblond. Then we examine the nonrelativistic version of the linear Dirac wave equation. With an Abelian gauge field we find, in a weak field approximation, the Pauli equation as well as the spin—orbit interaction and a part reminiscent of the Darwin term. We also propose a generalized model involving the interaction of the Dirac field with a non-Abelian gauge field; the SU(2) Hamiltonian is given as an example.     

A YANG–MILLS ELECTRODYNAMICS THEORY ON THE HOLOMORPHIC TANGENT BUNDLE

Considering a complex Lagrange space ([24]), in this paper the complex electromagnetic tensor fields are defined as the sum between the differential of the complex Liouville 1-form and the symplectic 2-form of the space relative to the adapted frames of the Chern–Lagrange complex nonlinear connection. In particular, an electrodynamics theory on a complex Finsler space is obtained.

We show that our definition of the complex electrodynamics tensors has physical meaning and these tensors generate an adequate field theory which offers the opportunity of coupling with the gravitation. The generalized complex Maxwell equations are written.

A gauge field theory of electrodynamics on the holomorphic tangent bundle is put over T′M and the gauge invariance to phase transformations is studied. An extension of the Dirac Lagrangian on T′M coupled with the electrodynamics Lagrangian is studied and it offers the framework for a unified gauge theory of fields.     

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.     

Determination of Phase Space Spectra of the Generalized Chiral Schwinger model with the Lorentz invariant Mass like Term for the Choice a − r2 = 0

We have considered the generalized version of chiral schwinger model with the Lorentz covariant masslike term for gauge field with the choice a ? r² =?0. We carry out the quantization by the canonical Dirac method of both the gauge-invariant and non-invariant version of this model to determine the phase space structure. Therefore we have shown that the gauge invariant theory has the same physical spectrum as that of the original gauge noninvariant formulation.

     

Gauge theories with minimal subtraction and the decoupling theorem

We show explicitly, to the two-loop level, that the decoupling theorem of Appelquist and Carazzone is valid, and a consistent light effective field theory exists, for quantum electrodynamics in arbitrary α-gauges, and non-abelian gauge theory in α = 0, Landau gauge, renormalized by minimal subtraction.     

Gauge theories on the $\kappa$-Minkowski spacetime

This study of gauge field theories on -deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the concept of enveloping algebra-valued gauge transformations and the Seiberg-Witten formalism. Derivative-valued gauge fields lead to field strength tensors as the sum of curvature- and torsion-like terms. We construct the Lagrangians explicitly to first order in the deformation parameter. This is the first example of a gauge theory that possesses a deformed Lorentz covariance.Received: 17 December 2003, Revised: 6 May 2004, Published online: 23 June 2004     

Geometrization of the Gauge Connection within a Kaluza–Klein Theory

We geometrize a generic (abelian and non-abelian) gauge coupling within the framework of a Kaluza–Klein theory, by choosing a suitable matter-field dependence on the extra coordinates. We first extend the Nöther theorem to a multidimensional spacetime, the Cartesian product of a 4-dimensional Minkowski space and a compact homogeneous manifold (whose isometries reflect the gauge symmetry). On such a “vacuum” configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra for a spacetime with the Kaluza–Klein restrictions. By splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms arise.     

Non-Abelian Gauge Theories on Non-Commutative Spaces

The construction of a non-abelian gauge theory on non-commutative spaces is based on enveloping algebra-valued gauge fields. The number of independent field components is reduced to the number of gauge fields in a usual gauge theory. This is done with the help of the Seiberg–Witten map. The dynamics is formulated with a Lagrangian where additional couplings appear. Received: 9 August 2000 / Accepted: 12 August 2000     

Analytic Tools to Brane Technology in N = 2 Gauge Theories with Matter

Exact solutions to the low-energy effective action (LEEA) of the four-dimensional N = 2 supersymmetric gauge theories are known to be obtained either by quantum field theory methods from S-duality in the Seiberg-Witten approach, or by the Type-IIA superstring/M-Theory methods of brane technology. After a brief review of the standard field-theoretical results for the N = 2 gauge (Seiberg-Witten) LEEA, we consider a field-theoretical derivation of the exact hypermultiplet LEEA by using the N = 2 harmonic superspace methods. We illustrate our techniques on a number of explicit examples. Our main purpose, however, is to discuss the existing analytical (calculational) support for the alternative methods of brane technology. We summarize known exact solutions to the eleven-dimensional and ten-dimensional type-IIA supergravities, which describe classical configurations of intersecting BPS branes with eight supercharges relevant to the non-perturbative N = 2 gauge theory with fundamental hypermultiplet matter. The crucial role of the M-Theory in providing a classical resolution of singularities in the ten-dimensional (Type-IIA superstring) brane picture, as well as the N = 2 extended supersymmetry in four dimensions, are made manifest. The two approaches to a derivation of the exact N = 2 gauge theory LEEA are thus seen to be complementary to each other and mutually dependent.     

Non-abelian vortices on surfaces and their statistics

We discuss the physics of topological vortices moving on an arbitrary surface M in a YangMills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or non-orientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is non-abelian.     

Gauge dependence of renormalization group parameters in ghost-free non-abelian gauge theories

We discuss the gauge dependence of the renormalization group parameters in a class of ghost-free non-abelian gauge theories. We show, using the n-dimensional regularization with the “minimal” renormalization procedure, that these parameters are gauge independent.