Gauge-invariant quark and gluon fields in QCD: dynamics, topology, and the Gribov ambiguity

TL;DR

This paper explores gauge-invariant formulations of QCD, focusing on the construction of gauge-invariant fields, their topological properties, and the presence of Gribov copies, aiming to improve understanding of low-energy phenomena.

Contribution

It introduces a method to express QCD in terms of gauge-invariant fields and investigates their topological features and Gribov ambiguities in the temporal gauge.

Findings

Gauge-invariant fields exhibit Gribov copies.

Relation established between Hamiltonians in different gauges.

Topological properties of gauge-invariant fields analyzed.

Abstract

We review the implementation, in a temporal-gauge formulation of QCD, of the non-Abelian Gauss's law and the construction of gauge-invariant gauge and matter fields. We then express the QCD Hamiltonian in terms of these gauge-invariant operator-valued fields, and discuss the relation of this Hamiltonian and the gauge-invariant fields to the corresponding quantities in a Coulomb gauge formulation of QCD. We argue that a representation of QCD in terms of gauge-invariant quantities could be particularly useful for understanding low-energy phenomenology. We present the results of an investigation into the topological properties of the gauge-invariant fields, and show that there are Gribov copies of these gauge-invariant gauge fields, which are constructed in the temporal gauge, even though the conditions that give rise to Gribov copies do not obtain for the gauge-dependent temporal-gauge fields.