On the structure of the residual gauge orbit

TL;DR

This paper investigates the structure of gauge orbits and the Gribov-Singer ambiguity, exploring how averaging over Gribov copies can be used in non-perturbative gauge fixing to ensure consistent correlation functions across different methods.

Contribution

It analyzes the properties of gauge orbits and discusses the potential of averaging over Gribov copies in non-perturbative gauge fixing to improve comparability.

Findings

Properties of gauge orbits are characterized.

Averaging over Gribov copies may help in non-perturbative gauge fixing.

Implications for lattice and continuum gauge theories are discussed.

Abstract

Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to ensure comparability. Beyond perturbation theory, this is complicated by the Gribov-Singer ambiguity. In principle, lattice gauge theory can manipulate individual Gribov copies, thus making it an excellent method to deal with the ambiguity. However, to compare to continuum methods this requires to replicate the same treatment outside the lattice, usually in a path integral formulation. Here, the properties of the gauge orbit will be investigated with respect to this question. Especially, the possibility of employing averages over Gribov copies in non-perturbative generalizations of the Landau gauge will be discussed.