Revisiting the Wu-Yang approach to magnetic charge

TL;DR

This paper extends the Wu-Yang approach to magnetic charge by introducing a disk-like current and magnetic field, revealing new insights into electromagnetic field momentum and its physical implications.

Contribution

It introduces a disk-like current density in the Wu-Yang framework, connecting it to magnetic flux and field momentum, and compares it with the Dirac string and Banderet monopole potentials.

Findings

Disk magnetic field mimics Dirac string flux

Electric charges near the disk induce electromagnetic field momentum

Non-singular Banderet monopole also exhibits magnetic flux and momentum

Abstract

The Wu-Yang fiber bundle approach to magnetic charge is extended with a disk-like sheet current density and associated magnetic field in the overlap region between the Northern hemisphere and Southern hemisphere, where the different vector potentials connect. This disk magnetic field plays a role similar to the Dirac string in the Dirac approach to magnetic charge - it brings an inward magnetic flux of $4 \pi g$ which then gives rise to an outward Coulomb magnetic flux of $4 \pi g$. As with the Dirac string approach we show that placing an electric charge near this disk magnetic field gives rise to a non-zero electromagnetic field momentum. We discuss some of the possible physical consequences of this electromagnetic field momentum. We conclude by showing that the non-singular, but non-single valued Banderet monopole potential also has a disk-like magnetic flux and non-zero electromagnetic field momentum in the presence of an electric charge.