A Maxwell field minimally coupled to torsion

TL;DR

This paper explores how a Maxwell field minimally coupled to torsion within Einstein-Cartan gravity modifies electromagnetic properties, potentially acting like magnetic monopoles and influencing charge quantization at high energies.

Contribution

It derives explicit formulas for torsion and electromagnetic tensors in the presence of torsion and discusses the implications of photon-torsion coupling breaking gauge invariance.

Findings

Divergence of magnetic field is non-zero due to torsion.

Photon-torsion coupling acts like an effective magnetic monopole density.

Coupling is significant only at extremely high energies in early Universe or black holes.

Abstract

We consider the Lagrangian density for a free Maxwell field, in which the electromagnetic field tensor minimally couples to the affine connection, in the Einstein-Cartan-Sciama-Kibble theory of gravity. We derive the formulae for the torsion and electromagnetic field tensors in terms of the electromagnetic potential. The divergence of the magnetic field does not vanish: the photon-torsion coupling acts like an effective magnetic monopole density. Such a coupling, which breaks U(1) gauge invariance, is significant only at extremely high energies existing in the very early Universe or inside black holes. It may, however, provide a mechanism for Dirac's quantization of electric charge.