Chern-Simons electrodynamics in (2+1)-spacetime with torsion

TL;DR

This paper explores how Chern-Simons electrodynamics behaves in a (2+1)-dimensional spacetime with torsion, revealing unique relationships between torsion, the CS field, and electromagnetic properties.

Contribution

It introduces torsion into Chern-Simons electrodynamics and analyzes its effects, showing the photon mass remains unaffected by torsion, unlike in earlier models.

Findings

Chern-Simons field is proportional to scalar field squared times torsion.

Electric field is proportional to torsion vector.

Photon mass is independent of torsion in this model.

Abstract

Chern-Simons electrodynamics in 2+1-spacetimes with torsion is investigated. We start from the usual Chern-Simons (CS) electrodynamics Lagrangian and Cartan torsion is introduced in the covariant derivative and by a direct coupling of torsion vector to the CS field. Variation of the Lagrangian with respect to torsion shows that Chern-Simons field is proportional to the product of the square of the scalar field and torsion. The electric field is proportional to torsion vector and the magnetic flux is computed in terms of the time-component of the two dimensional torsion. Contrary to early massive electrodynamics in the present model the photon mass does not depend on torsion.