Gribov Problem and BRST Symmetry

TL;DR

This paper explores the Gribov problem in gauge theories, discussing how BRST symmetry can be maintained when summing over Gribov copies, and examines the implications for gauge fixing and symmetry stability.

Contribution

It introduces a specific criterion for formulating BRST-invariant path integrals in the presence of Gribov copies and analyzes a soluble gauge model illustrating this approach.

Findings

A path integral formulation with BRST symmetry is possible under a global single-valuedness condition.

A soluble gauge model with Gribov copies is discussed as an example.

The connection between BRST instability and the Gribov problem is considered.

Abstract

After a brief historical comment on the study of BRS(or BRST) symmetry , we discuss the quantization of gauge theories with Gribov copies. 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 $\tau (x) = f( A_{\mu}^{\omega}(x))$ is ``globally single valued'', where $f( A_{\mu}^{\omega}(x)) = 0 $ specifies the gauge condition. As an example of the theory which satisfies this criterion, we comment on a soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren. We also comment on a possible connection of the dynamical instability of BRST symmetry with the Gribov problem on the basis of an index notion.