Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D spacetime variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.      

A one-dimensional invariance principle for gauge fields of integer spin

A relativistic two-particle system is analyzed in which the particles are bound by an harmonic oscillator potential. The system is invariant under τ-reparametrizations as well as under two gauge transformations of the coordinates. The corresponding first-class constraints give a BRST charge which can be used to construct a classical field theory action for all integer spin gauge fields.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

Renormalization in non-Abelian gauge theories

The renormalization is performed in a manifestly covariant approach. The simplest form of the Ward identities z₁=z₂=…=z_n=… is fulfilled automatically in every gauge. In the Yang-Mills theory the counter-terms are gauge-invariant and depend on the charge renormalization constant only. In pure gravitation the analysis of all divergences is reduced in the present approach to some special classification of the kth order scalar densities in a Riemannian space.     

Isotropization times in non-Abelian gauge theory

We consider non-perturbative estimates of isotropization times for gauge theory on a lattice, relevant for the discussion of thermalization in collisions of heavy nuclei.     

Poincaré gauge invariance and the dynamical role of spin in gravitational theory

We classify, according to the number of independent gauge fields, Poincaré gauge invariant theoretical frameworks of describing gravity into three categories. One of them may provide the dynamical definition of the spin tensor S and that of the energy-momentum tensor T, resulting in the response equation of matter to gravity with the gravitational field strengths, D′ and F, coupled to the former tensors

$\text{T}{}_{\mathrm{\nu }}{}^{\mathrm{\mu }}\text{;}{}_{\mathrm{\mu }}\text{=D′}{}_{\mathrm{\mu \lambda \nu }}\text{T}{}^{\mathrm{\mu \lambda }}\text{+F}{}_{\mathrm{\mu \lambda \nu \rho }}\text{S}{}^{\mathrm{\rho \mu \lambda }}$

, where the right-hand side represents spin force densities. In the absence of spin the response reduces to the conventional one of general relativity, i.e., without the spin forces. For the electromagnetic field the phase-gauge invariance requires the same conclusion as for a scalar field. For a spin $\text{1}\text{2}$ particle there is torsion, which deflects its trajectory from geodesic; an explicit expression for torsion takes a simple form of the axial vector current $\text{ψ}\text{γ}{}_5\text{γ}{}_{\mathrm{k}}\text{ψ}$.     

Multi-meson exchange in non-Abelian gauge theories

We find a new sum rule for the residue of the J = 0 fixed pole in Compton scattering. The sum rule applies to any target and links the residue to a calculable set of contributions from the resonance region. We discuss proton, neutron, deutron and pion targets and the possibility of discriminating from previous models. The relationship with the parton model is noted and the feasibility of measuring pion photoabsorption cross sections is discussed.     

Differentiable probabilities: A new viewpoint on spin,gauge invariance,gauge fields,and relativistic quantum mechanics

A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model.     

Magnetic monopoles and non-Abelian gauge theories

We review some properties of magnetic monopoles in non-Abelian gauge theories. Removal of Dirac string singularities and generalizations of the Wu-Yang solution that follow from this procedure are described. A discussion of the possible relevance of monopoles in strong interaction models and their role in quark confinement schemes is given. The magnetic monopole soliton discovered by 't Hooft and Polyakov, the first order formalism developed by Bogomolny, and extensions of these ideas are illustrated.Work supported in part by the U.S. Energy Research and Development Administration under Contract No. EY-76-C-02-2232B^*000.     

Self-interaction and gauge invariance

A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g. chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases, they are determined by the conserved currents associated with the initial (linear) gauge invariance of the first kind. Use of first-order formalism leads uniformly to a simple cubic self-interaction.Supported by USAF OAR under Grant AFOSR 70-1864.     

Multispin particles and non-Abelian tensor gauge fields

A system of tensorial equations is suggested as a bipotential generalization of the Stückelberg equations written for spin-tensors. These equations describe particles having two spin states: 1/2 and 3/2 (particles with the multispin 1/2, 3/2). The Lagrangian of the theory is invariant under the transformations of the field variables forming a group U(1) SO (4, 2) SO (4, 2). Localization of the transformation parameters of this group of internal symmetry leads to introduction of a non-Abelian gauge field carrying the maximal spin 2. A possible physical interpretation of a multispin particle theory is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 78–81, November, 1982.The authors are thankful to I. S. Satsunkevich and L. F. Zhirkov for useful discussion of some questions considered above.     

VII. Difficulties in fixing the gauge in non-Abelian gauge theories

Some problems arising from the use of the Coulomb gauge in SU(2) Yang-Mills theory are discussed. It is shown that: i) the transversality condition does not fix the gauge uniquely (Gribov ambiguity); ii) there exist physical configurations that cannot be described by a continuous A_μ in the Coulomb gauge.     

Problems related to gauge invariance and momentum,spin decomposition in nucleon structure study

How do the quark and gluon share the nucleon momentum? How does the nucleon spin distribute among its constituents? What means the quark and gluon momentum, spin and orbital angular momentum? These problems are analyzed and a solution is proposed based on gauge invariance principle, canonical quantization rule and Poincaré covariance.     

On the concept of spontaneously broken gauge symmetry in condensed matter physics

We discuss the concept of spontaneous breaking of gauge symmetry in super-conductors and superfluids and, in particular, the circumstances under which the absolute phase of a superfluid can be physically meaningful and experimentally relevant. We argue that the study of this question pushes us toward the frontiers of what we understand about the quantum measurement process, and underline the need for a new theoretical framework that keeps pace with modern technological capabilities.     

MuSR技术在凝聚态物理中的应用

缪子自旋弛豫/旋转(MuSR)实验技术利用缪子的自旋,在原子尺度上研究样品内部磁场的静态分布和动态涨落。文章介绍MuSR实验技术在凝聚态物理中的应用,阐述了MuSR在磁性、超导材料中发现的独特信息,包括磁有序、内部磁场分布、具有特定频率范围的自旋涨落,以及在半导体材料中获得杂质的电子状态和位置。这些应用表明 MuSR 对于理解关联电子材料复杂的物理现象及其物理机制具有重要意义。     

Composite hadrons in non-Abelian lattice gauge theories

Euclidean non-Abelian gauge theories are quantized on a (finite) lattice using functional integration. From the general from of the 2m-point Schwinger function for the fundamental fermions fields, dynamical consequences for composite meson and fermion fields are investigated. The Okubo-Zweig-Iizuka rule is derived and an analogy to non-relativistic potentials for the quark-antiquark and the 3-quark system is exhibited.