Resolving temporal Gribov copies in Coulomb gauge Yang-Mills theory

TL;DR

This paper addresses the issue of temporal Gribov copies in Coulomb gauge Yang-Mills theory, showing that accounting for zero-modes enforces a zero total color charge and effectively fixes the gauge.

Contribution

It provides a detailed analysis of temporal zero-modes in the Faddeev-Popov operator, leading to a consistent gauge fixing in Coulomb gauge Yang-Mills theory.

Findings

Zero total color charge constraint derived

Effective gauge fixing once Gauss' law is resolved

Explicit treatment of temporal zero-modes in the functional integral

Abstract

The continuum Yang-Mills functional integral within the first order formalism and in Coulomb gauge is studied. In particular, the temporal zero-modes of the Faddeev-Popov operator are explicitly accounted for. It is shown that the treatment of these zero-modes results in the constraint that the total color charge of the system vanishes at all times. Further, it is argued that the functional integral is effectively fully gauge-fixed once Gauss' law has been resolved in Coulomb gauge.