The Relationship of the Laplacian Gauge to the Landau Gauge

TL;DR

This paper explores the connection between Laplacian and Landau gauges in SU(N) gauge theories, showing their equivalence at lowest order and differences at higher orders through perturbative analysis and numerical examination.

Contribution

It demonstrates the perturbative relationship between Laplacian and Landau gauges and provides numerical evidence of their divergence beyond leading order.

Findings

Laplacian gauge configurations satisfy Landau gauge at O(g^1).

Numerical results show divergence from Landau gauge at O(g^2).

Laplacian gauge is perturbatively related to Landau gauge at lowest order.

Abstract

The Laplacian gauge for gauge group SU(N) is discussed in perturbation theory. It is shown that to the lowest non-trivial order, O(g^1), configurations in the Laplacian gauge automatically satisfy the (finite difference) Landau gauge condition. Laplacian gauge fixed configurations are examined numerically and it is seen that to O(g^2) they do not remain in the Landau gauge.