Spacetime symmetries of the Lorentz-violating Maxwell-Chern-Simons model

TL;DR

This paper investigates the spacetime symmetry properties of a modified electrodynamics model with a Chern-Simons term, revealing an enhanced symmetry structure under specific conditions related to the external vector.

Contribution

It identifies the full spacetime symmetry group of the Lorentz-violating Maxwell-Chern-Simons model, including an additional SIM(2) symmetry when the external vector is lightlike.

Findings

The model has translation invariance and a little group of symmetries.

An extra spacetime symmetry exists if the external vector is lightlike.

The symmetry group is identified as SIM(2).

Abstract

The spacetime symmetries of classical electrodynamics supplemented with a Chern-Simons term that contains a constant nondynamical 4-vector are investigated. In addition to translation invariance and the expected three remaining Lorentz symmetries characterized by the little group of the external vector, the model possesses an additional spacetime symmetry if the nondynamical vector is lightlike. The conserved current associated with this invariance is determined, and the symmetry structure arising from this invariance and the usual little group ISO(2) is identified as SIM(2).