The Berry Phase and Monopoles in Gluodynamics

TL;DR

This paper presents a gauge invariant method to define monopoles in gluodynamics using Wilson loops, providing an explicit construction applicable in both continuum and lattice formulations.

Contribution

It introduces a novel gauge invariant monopole definition based on Wilson loops and a U(1) group, advancing monopole studies in lattice gauge theories.

Findings

Gauge invariant monopole definition on the lattice.

Explicit construction in continuum and lattice formulations.

Preservation of gauge invariance in monopole charge definition.

Abstract

We introduce a gauge invariant definition of a monopole on the lattice. The construction is based on the observation that for each Wilson loop there exists an extra U(1) group which leaves the loop invariant. Since the lattice formulation utilizes the language of Wilson loops, the definition of the monopole charge in terms of this plaquette dependent U(1) is gauge invariant. The explicit construction of gauge invariant monopoles is presented both in continuum and on the lattice.