Feynman gauge on the lattice: new results and perspectives

TL;DR

This paper presents a new lattice implementation of the Feynman gauge based on a functional extension of the Landau gauge, discusses convergence issues due to discretization, and proposes solutions involving alternative discretizations or larger gauge groups.

Contribution

It introduces a novel lattice Feynman gauge implementation that maintains continuum properties and explores methods to address discretization convergence problems.

Findings

The new implementation preserves continuum gauge properties.

Discretization causes convergence issues due to bounded gluon fields.

Proposed solutions include alternative discretizations and larger gauge groups.

Abstract

We have recently introduced a new implementation of the Feynman gauge on the lattice, based on a minimizing functional that extends in a natural way the Landau-gauge case, while preserving all the properties of the continuum formulation. The only remaining difficulty with our approach is that, using the standard (compact) discretization, the gluon field is bounded, while its four-divergence satisfies a Gaussian distribution, i.e. it is unbounded. This can give rise to convergence problems when a numerical implementation is attempted. In order to overcome this problem, one can use different discretizations for the gluon field, or consider an SU(N_c) group with sufficiently large N_c. Here we discuss these two possible solutions.