Properties of a consistent Lorentz-violating Abelian gauge theory

TL;DR

This paper proposes a Lorentz-violating modification to massless QED with higher order derivatives, analyzes fermion mass generation, and discusses the model's consistency and implications for the effective speed of light.

Contribution

It introduces a consistent Lorentz-violating Abelian gauge theory with higher order derivatives and studies its perturbative properties and fermion mass generation mechanisms.

Findings

Fermion dynamical mass generation is demonstrated.

The model remains consistent at higher-order loops.

Fermions experience an effective light cone with a maximum speed less than c.

Abstract

A Lorentz violating modification of massless QED is proposed, with higher order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach. Perturbative properties of the model are calculated at one-loop and discussed at higher-order loops, showing the consistency of the model. We explain that there is no contradiction with the definition of the speed of light c, although fermions see an an effective light cone, with a maximum speed smaller than c.