On embeddings of gauge groups in Yang-Mills theory

We discuss some group theoretical properties of Yang-Mills theories. We consider conditions necessary and sufficient to decide if the gauge field is reducible and prove some related theorems. We give criteria for embeddings and work out the case of SU (3) explicitly.     

Yang-Mills gauge theory and gravitation

We point out that Yang's and Einstein's gravitational equations can be obtained from a geometric approach of Yang-Mills gauge theory in a sourceless case, under a decomposition of the Poincaré algebra. Otherwise, Einstein's equations cannot be derived from a Yang-Mills gauge equation when sources are inserted in the rotational sector of that algebra. A gauge Lagrangian structure is also discussed.     

Gravity as Yang-Mills gauge theory

We propose a Yang-Mills field theory of gravity based on a unitary phase-gauge-invariance of the lagrangian where the gauge transformations are those of the SU(2) × U(1) symmetry of the 2-spinors. In the classical limit this microscopic theory results in Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version.     

Some properties of orbit space in Yang-Mills theory

In Yang-Mills theory, it is shown that the Ricci tensor in the orbit space is always positively defined. Nevertheless, the orbit space cannot be considered as compact because it contains infinite-dimensional Euclidean hypersurfaces.     

Verifying the Kugo-Ojima confinement criterion in Landau gauge Yang-Mills theory

Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills theory.     

The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge

The Dyson-Schwinger equation for the ghost-gluon vertex of the Hamiltonian approach to Yang-Mills theory in Coulomb gauge is solved at one-loop level using as input the non-perturbative ghost and gluon propagators previously determined within the variational approach. The obtained ghost-gluon vertex is IR finite but IR enhanced compared to the bare one by 15%-25%, depending on the kinematical momentum regime.     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.     

The orbit space of the action of gauge transformation group on connections

The behaviour of orbits of the action of the group of smooth gauge transformations on connections for a principal bundle P(M, G) is discussed with and without compactness assumption on M and G. In the case of compact M and with suitable conditions on G a stratification structure for the space of orbits is established. A natural tame weak Riemannian metric is given on each stratum.     

The gauge fixing problem around classical solutions of the Yang-Mills theory

We show that the Gribov problem [1] does not exist for small deformations of an irreducible gauge potential, in the covariant background gauge. This justifies gauge fixing within the framework of perturbation expansion. In proving the existence of local gauge sections we investigate the global orbit structure around an irreducible gauge potential.     

Construction of physical states in Yang-Mills theory: The time-like gauge

We construct physical states in pure Yang-Mills theory in the time-like gauge A_α⁰ = 0. We also construct a complete basis in the physical subspace of Hilbert space. Comparison is made with a recent paper by Eylon.     

On the Yang-Mills effective action with instanton gauge field

The calculation of the determinant for the second order covariant derivative operator is analyzed in the space R⁴ and for Yang-Mills instanton field configurations. The problems inherent to the ultraviolet ζ-function renormalization method and infrared divergencies of this operator are reviewed. A method for estimating the asymptotic coefficients of its determinant has been discussed and the failure of the general conformal invariance induced by any regularization technique has also been considered. A particular solution valid for a Yang-Mills multi instanton configuration, valuable in order to get the non conformally invariant piece of the general solution, is the main result obtained here. We give it as an integral equation, namely in a semi-explicit form.     

The Yang-Mills fields — from the gauge theory to the mechanical model

The paper presents some mechanical models of gauge theories, i.e. gauge fields transposed in a space with a finite number of degree of freedom. The main focus is on how a global symmetry as the BRST one could be transferred in this context. The mechanical Yang-Mills model modified by taking the ghost type variables into account will be considered as an example of nonlinear dynamical systems.      

Path integral on a group manifold and the lattice gauge theory Hamiltonian

For a quantum mechanical system living on the manifold of a compact simple Lie group we present explicit formulae for the quantum corrections, both in the Hamiltonian and, for the most common time discretization, in the path integral. As a special application of this rather general procedure, we compare, for lattice gauge theories, the path integral corresponding to the Kogut-Susskind Hamiltonian and the Wilson action. The latter is shown to correspond to a very special but elegant way of discretizing the time variable.