Zwanziger-Landau gauge in regularized gauge theory

The Green functions of Zwanziger-gaugefixed and continuum-regularized gauge theory are finite and transverse to all orders as the Zwanziger parameter α goes to zero.     

Simplicial gauge theory and quantum gauge theory simulation

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of β.     

Local and global gauge symmetries in temporal gauge

In the temporal gauge formalism, in order to make a distinction between the global limit of local gauge transformations and global ones a non-local operator, θ, is introduced. It is claimed that what kind of θ is used is equivalent to what kind of gauge-fixing schemes is chosen. Along this idea, in non-abelian theories the coulomb, axial and unitary gauges have been investigated. In the unitary gauge spontaneous breakdown of global gauge symmetry has been found to be reduced to a problem of the boundary condition for the Higgs field and the occurrence of symmetry breaking has been concluded.     

Non-abelian gauge couplings in thermal gauge field theories

Properties of the effective gauge couplings renormalized at finite temperature and density in thermal non-abelian gauge field theories are studied within one-loop approximations. Strong and severe vertex dependence is shown to come out both in the temperature and chemical potential dependences. Difficulties appearing in the perturbative calculation of physical quantities, indicated by the above disaster, are discussed. Also discussed is what insight might be gained from the present analysis into the “magnetic” screening of effective charge.     

Residual gauge invariance of Hamiltonian lattice gauge theories

The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegenbauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically.     

The radiation gauge static potential for non-abelian gauge fields

The static potential between a fermion and an anti-fermion in a group singlet state is calculated, through two loops, in the radiation gauge first order formalism. The results of this calculation imply that the Coulomb propagator is not sufficient to determine the static potential: a new function of the coupling constant α_s(?t) is also required.     

Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.     

The Kirchhoff gauge

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge, the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.     

Gravitational gauge mediation

It is often the case that the naive introduction of the messenger sector to supersymmetry breaking models causes restoration of supersymmetry. We discuss a possibility of stabilizing the supersymmetry breaking vacuum by gravitational interaction.     

Conformal gauge mediation

We propose a one-parameter theory for gauge mediation of supersymmetry (SUSY) breaking. The spectrum of SUSY particles such as squarks and sleptons in the SUSY standard-model and the dynamics of SUSY-breaking sector are, in principle, determined only by one parameter in the theory, that is, the mass of messengers. Above the messenger threshold all gauge coupling and Yukawa coupling constants in the SUSY-breaking sector are on the infrared fixed point. We find that the present theory may predict a split spectrum of the standard-model SUSY particles, mgaugino<msfermion$m_{\mathrm{gaugino}}<m_{\mathrm{sfermion}}$, where mgaugino$m_{\mathrm{gaugino}}$ and msfermion$m_{\mathrm{sfermion}}$ are SUSY-breaking masses for gauginos and squarks/sleptons, respectively.     

Determination of a gauge transformation group in gauge field theory

The existence of different types of gauge transformations in gauge theory and the theory of gravitation is established and they are defined in the language of fiber bundles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 52–57, December, 1984.     

Functional integration and gauge ambiguities in generalized abelian gauge theories

We consider the covariant quantization of generalized abelian gauge theories on a closed and compact n$n$-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger–Simons differential characters. The space of gauge fields is shown to be a non-trivial bundle over the orbits of the subgroup of smooth Cheeger–Simons differential characters. Furthermore each orbit itself has the structure of a bundle over a multi-dimensional torus. As a consequence there is a topological obstruction to the existence of a global gauge fixing condition. A functional integral measure is proposed on the space of gauge fields which takes this problem into account and provides a regularization of the gauge degrees of freedom. For the generalized p$p$-form Maxwell theory closed expressions for all physical observables are obtained. The Green’s functions are shown to be affected by the non-trivial bundle structure. Finally the vacuum expectation values of circle-valued homomorphisms, including the Wilson operator for singular p$p$-cycles of the manifold, are computed and selection rules are derived.     

Coulomb gauge vacua of SU(3) gauge theory

SU(3) gauge field theory is studied in the Coulomb gauge, and the topologically distinct, but gauge equivalent, vacuum configurations are analysed. Considering the gauge transformations of the form U ε U(2) ?SU(3)/U(2), we have obtained a new class of vacuum fields characterized by the topological quantum number η = ±1.     

A quasi-temporal gauge

We prove that a complete fixing of the temporal gauge,A _o =0, in which one imposesa subsidiary gauge condition, such as, for instance ?_i A _i (x,t ₀) = 0 leads to consistent formulation of the theory with simple Feynman rulesand a well defined gluon propagator. The correct exponentiation of the time dependence of the Wilson loop has been checked to occur up to order g⁴.