On Dirac-like Monopoles in a Lorentz- and CPT-violating Electrodynamics

TL;DR

This paper investigates magnetic monopoles within a Lorentz- and CPT-violating extension of electrodynamics, revealing how monopoles affect charge conservation, duality, and force asymmetries due to the added Chern-Simons-like term.

Contribution

It introduces a consistent framework for monopoles in Lorentz- and CPT-violating electrodynamics, analyzing charge conservation, duality breaking, and force asymmetries, including a quantization condition in reduced dimensions.

Findings

Charge conservation can be maintained with an induced electric current.

Duality symmetry is broken by the Lorentz-violating term.

An asymmetry appears in electromagnetic forces on electric and magnetic sources.

Abstract

We study magnetic monopoles in a Lorentz- and CPT-odd electrodynamical framework in (3+1) dimensions. This is the standard Maxwell model extended by means of a Chern-Simons-like term, $b_\mu\tilde{F}^{\mu\nu}A_\nu$ ($b_\mu$ constant), which respects gauge invariance but violates both Lorentz and CPT symmetries (as a consequence, duality is also lost). Our main interest concerns the analysis of the model in the presence of Dirac monopoles, so that the Bianchi identity no longer holds, which naively yields the non-conservation of electric charge. Since gauge symmetry is respected, the issue of charge conservation is more involved. Actually, the inconsistency may be circumvented, if we assume that the appearance of a monopole induces an extra electric current. The reduction of the model to (2+1) dimensions in the presence of both the magnetic sources and Lorentz-violating terms is presented. There, a quantization condition involving the scalar remnant of $b_\mu$, say, the mass parameter, is obtained. We also point out that the breaking of duality may be associated with an asymmetry between electric and magnetic sources in this background, so that the electromagnetic force experienced by a magnetic pole is supplemented by an extra term proportional to $b_\mu$, whenever compared to the one acting on an electric charge.