BRST Symmetric Formulation of a Theory with Gribov-type Copies

TL;DR

This paper develops a BRST symmetric path integral formulation for theories with Gribov copies, analyzing a soluble model to ensure gauge independence and discussing implications for non-Abelian gauge theories like QCD.

Contribution

It introduces a specific BRST formulation for models with Gribov copies and provides a detailed analysis of a soluble model satisfying the global single-valuedness criterion.

Findings

BRST symmetry ensures gauge independence of physical quantities.

Vacuum state and perturbative corrections analyzed via BRST symmetry.

Implications for Gribov problem in non-Abelian gauge theories discussed.

Abstract

A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between $\tau$ and the gauge parameter $\omega$ defined by $\tau (x) = f( A_{\mu}^{\omega})$ is ``globally single valued'', where $f( A_{\mu}^{\omega}) = 0 $ specifies the gauge condition. A soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren satisfies this criterion. A detailed BRST analysis of the soluble model proposed by the above authors is presented. The BRST symmetry, if it is consistently implemented, ensures the gauge independence of physical quantities. In particular, the vacuum (ground) state and the perturbative corrections to the ground state energy in the above model are analysed from a view point of BRST symmetry and $R_{\xi}$-gauge. Implications of the present analysis on some aspects of the Gribov problem in non-Abelian gauge theory, such as the $1/N$ expansion in QCD and also the dynamical instability of BRST symmetry, are briefly discussed.