Investigation of Laplacian Gauge Fixing for U(1) and SU(2) Gauge Fields

TL;DR

This paper numerically investigates Laplacian gauge fixing for U(1) and SU(2) gauge fields, addressing Gribov ambiguities and comparing results to Landau gauge to evaluate its effectiveness as an alternative.

Contribution

It demonstrates that Laplacian gauge fixing performs well in practice and can serve as a viable alternative to Landau gauge fixing for lattice gauge theories.

Findings

Laplacian gauge fixing effectively addresses Gribov ambiguities.

Comparisons show Laplacian gauge produces smooth configurations similar to Landau gauge.

Laplacian gauge fixing is practical and reliable for U(1) and SU(2) fields.

Abstract

The Laplacian gauge on the lattice is investigated numerically using U(1) and SU(2) gauge fields. The problem of Gribov ambiguities is addressed and to asses the smoothness of the gauge fixed configurations, they are compared to configurations fixed to the Landau gauge. The results of these comparisons with the Landau gauge indicate that Laplacian gauge fixing works very well in practice and offers a viable alternative to Landau gauge fixing.