Gauge fixing and Gribov copies in pure Yang-Mills on a circle

TL;DR

This paper investigates gauge fixing and Gribov copies in pure Yang-Mills theory on a cylindrical spacetime, revealing how different gauge fixing methods impact the Hamiltonian and spectra, with insights relevant for lattice gauge theories.

Contribution

It provides an explicit analysis of gauge fixing effects and Gribov copies in a simplified Yang-Mills model on a circle, comparing continuum and lattice approaches.

Findings

Different gauge fixing procedures yield different Hamiltonians and spectra.

Spectra coincide after a shift of states, indicating a form of equivalence.

Lattice gauge fixing issues are discussed in the context of the model.

Abstract

%In order to understand how gauge fixing can be affected on the %lattice, we first study a simple model of pure Yang-mills theory on a %cylindrical spacetime [$SU(N)$ on $S^1 \times$ {\bf R}] where the %gauge fixed subspace is explicitly displayed. On the way, we find that %different gauge fixing procedures lead to different Hamiltonians and %spectra, which however coincide under a shift of states. The lattice %version of the model is compared and lattice gauge fixing issues are %discussed. (---TALK GIVEN AT LATTICE 92---AMSTERDAM, 15 SEPT. 92)