SIM(2)-invariant Modifications of Electrodynamic Theory

TL;DR

This paper explores SIM(2)-invariant modifications to electrodynamics and quantum electrodynamics, allowing gauge fields to acquire mass and introducing new gauge transformation features within the framework of Very Special Relativity.

Contribution

It introduces SIM(2)-invariant modifications to Maxwell and QED theories, including gauge transformations and mass terms for gauge fields, expanding the theoretical landscape of electrodynamics.

Findings

Gauge fields with two polarization states can have nonzero mass.

Modified gauge transformations are consistent with SIM(2) invariance.

Proca-type equations are adapted for SIM(2)-covariant massive spin-1 particles.

Abstract

In the Cohen-Glashow Very Special Relativity we exhibit possible modifications to the Maxwell theory and to the quantum electrodynamics Lagrangian in some generality, and discuss characteristic features depending on the modifications. Modified gauge transformations in SIM(2)-invariant theories are introduced, and in these theories gauge fields with two polarization states can have nonzero mass. Also considered are SIM(2)-covariant modifications to the Proca-type field equations for a massive spin-1 particle.