Dirac and non-Dirac conditions in the 2-potential theory of magnetic charge

TL;DR

This paper explores a two-potential theory of magnetic charge with two scalar fields, revealing how symmetry breaking modifies Dirac conditions and affects electric and magnetic charge interactions.

Contribution

It introduces a detailed analysis of Dirac and non-Dirac conditions in a two-scalar-field magnetic charge model, highlighting the impact of symmetry breaking on charge quantization.

Findings

Magnetic photon acquires mass through symmetry breaking.

Dirac condition is modified to include magnetic photon mass.

Duality transformations reveal conditions for electric and magnetic charge decoupling.

Abstract

We investigate the Cabbibo-Ferrari, two potential approach to magnetic charge coupled to two different complex scalar fields, $\Phi_1$ and $\Phi_2$, each having different electric and magnetic charges. The scalar field, $\Phi_1$, is assumed to have a spontaneous symmetry breaking self interaction potential which gives a mass to the "magnetic" gauge potential and "magnetic" photon, while the other "electric" gauge potential and "electric" photon remain massless. The magnetic photon is hidden until one reaches energies of the order of the magnetic photon rest mass. The second scalar field, $\Phi _2$, is required in order to make the theory non-trivial. With only one field one can always use a duality rotation to rotate away either the electric or magnetic charge, and thus decouple either the associated electric or magnetic photon. In analyzing this system of two scalar fields in the Cabbibo-Ferrari approach we perform several duality and gauge transformations, which require introducing non-Dirac conditions on the initial electric and magnetic charges. We also find that due to the symmetry breaking the usual Dirac condition is altered to include the mass of the magnetic photon. We discuss the implications of these various conditions on the charges.