Lorentz gauge fixing and lattice QED

TL;DR

This paper investigates the Gribov ambiguity in lattice QED under Lorentz gauge, identifying key sources of gauge copies and emphasizing the importance of handling zero-momentum modes for accurate fermion mass estimates.

Contribution

It analyzes the origin of Gribov copies in lattice QED and demonstrates the necessity of removing zero-momentum modes for reliable gauge fixing and fermion mass calculations.

Findings

Gribov copies mainly caused by double Dirac sheets and zero-momentum modes

Removing these modes allows reaching the absolute extremum of the gauge functional

Proper treatment of zero-momentum modes is crucial for accurate fermion mass estimates

Abstract

The Gribov ambiguity problem is studied for compact lattice QED within the Lorentz gauge. In the Coulomb phase, Gribov copies are mainly caused by double Dirac sheets and zero-momentum modes of the gauge fields. Removing them by (non-) periodic gauge transformations allows to reach the absolute extremum of the Lorentz gauge functional. For standard Lorentz gauge fixing the Wilson fermion correlator turns out to be strongly effected by the zero-momentum modes. A reliable fermion mass estimate requires the proper treatment of these modes.