Linear Covariant Gauges on the Lattice

TL;DR

This paper discusses the formulation and analysis of linear covariant gauges on the lattice, providing a gauge-fixing procedure and results for the gluon propagator in SU(2) and two-dimensional cases.

Contribution

It introduces a lattice gauge-fixing method for linear covariant gauges that aligns with continuum definitions and applies it to SU(2) and 2D cases.

Findings

Gauge-fixing procedure successfully implemented on the lattice.

Results for the gluon propagator in 2D case obtained.

Method aligns with perturbative continuum definitions.

Abstract

Linear covariant gauges, such as Feynman gauge, are very useful in perturbative calculations. Their nonperturbative formulation is, however, highly non-trivial. In particular, it is a challenge to define linear covariant gauges on a lattice. We consider a class of gauges in lattice gauge theory that coincides with the perturbative definition of linear covariant gauges in the formal continuum limit. The corresponding gauge-fixing procedure is described and analyzed in detail, with an application to the pure SU(2) case. In addition, results for the gluon propagator in the two-dimensional case are given.