Gauge-invariant charged, monopole and dyon fields in gauge theories

TL;DR

This paper develops explicit methods to construct gauge-invariant Green functions for charged, monopole, and dyon fields in four-dimensional gauge theories, ensuring mathematical rigor and consistency with Dirac's flux quantization.

Contribution

It introduces a novel construction of gauge-invariant Green functions for monopoles and dyons, extending Dirac's proposals and applying to 't Hooft-Polyakov monopoles and Julia-Zee dyons.

Findings

Rigorous mathematical control for abelian lattice theories.

Construction of Green functions involves averaging over Mandelstam strings or flux tubes.

Connections discussed between the construction and semiclassical approaches.

Abstract

We propose explicit recipes to construct the euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed.