Comment on "Massive electrodynamics and the magnetic monopoles"

TL;DR

This paper corrects previous work on massive electrodynamics with magnetic monopoles, presenting a simple closed-form solution that reveals new features like the Dirac string becoming physical and potential modifications to the quantization condition.

Contribution

It provides a corrected, explicit solution for magnetic monopoles with photon mass, highlighting the physical nature of the Dirac string and symmetry breaking effects.

Findings

Dirac string becomes a physical feature of the solution

Photon mass breaks gauge and rotational symmetries

Potential alteration of the Dirac quantization condition

Abstract

In this paper we correct previous work on magnetic charge plus a photon mass. We show that contrary to previous claims this system has a very simple, closed form solution which is the Dirac string potential multiplied by a exponential decaying part. Interesting features of this solution are discussed, namely, (i) the Dirac string becomes a real feature of the solution, (ii) the breaking of gauge symmetry via the photon mass leads to a breaking of the rotational symmetry of the monopole's magnetic field, (iii) the Dirac quantization condition is potentially altered.