Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions

TL;DR

This paper addresses the challenge of defining the dispersion relation for Wilson fermions in lattice QCD, proposing a redefinition of fermionic kinematic momentum to resolve gauge-fixing related issues.

Contribution

It introduces a novel approach to redefine fermionic momentum, improving the consistency of dispersion relation calculations in gauge-fixed lattice QCD.

Findings

Identifies major difficulties in defining Wilson fermion dispersion relations.

Proposes a redefinition of fermionic kinematic momentum as a solution.

Enhances the reliability of gauge-fixed lattice QCD studies.

Abstract

We show that, when investigating Wilson-fermions correlation functions on the lattice, one is bound to encounter major difficulties in defining their dispersion relation, even at tree level. The problem is indeed quite general and, although we stumbled upon it while studying Coulomb-gauge applications, it also affects gauge fixed studies in covariant gauges, including their most popular version, Landau gauge. In this paper we will discuss a solution to this problems based on a redefinition of the kinematic momentum of the fermion.