What can we learn about Gribov copies from a formulation of QCD in terms of gauge-invariant fields?

TL;DR

This paper explores the structure of gauge-invariant fields in QCD within the temporal gauge, revealing how Gribov copies relate to topological sectors and the implementation of Gauss's law, providing insights into gauge fixing ambiguities.

Contribution

It introduces a method to construct gauge-invariant fields in temporal gauge QCD and analyzes their relation to Gribov copies and topological sectors.

Findings

Gribov copies exist in the temporal gauge when using gauge-invariant fields.

Gauge-invariant fields exhibit multiplicities linked to topological sectors.

Gribov copies are absent in the gauge-dependent formulation with unimplemented Gauss's law.

Abstract

We review the procedure by which we implemented the non-Abelian Gauss's law and constructed gauge-invariant fields for QCD in the temporal (Weyl) gauge. We point out that the operator-valued transformation that transforms gauge-dependent temporal-gauge fields into gauge-invariant ones has the formal structure of a gauge transformation. We express the ``standard'' Hamiltonian for temporal-gauge QCD entirely in terms of gauge-invariant fields, calculate the commutation rules for these fields, and compare them to earlier work on Coulomb-gauge QCD. We also discuss multiplicities of gauge-invariant temporal-gauge fields that belong to different topological sectors and that, in previous work, were shown to be based on the same underlying gauge-dependent temporal-gauge fields. We relate these multiplicities of gauge-invariant fields to Gribov copies. We argue that Gribov copies appear in the temporal gauge, but not when the theory is represented in terms of gauge-dependent fields and Gauss's law is left unimplemented. There are Gribov copies of the gauge-invariant gauge field, which can be constructed when Gauss's law is implemented.