Gauge symmetry and radiatively induced terms in dimension-5 non-minimal Lorentz-violating QED

TL;DR

This paper investigates gauge invariance and radiative effects in a non-minimal Lorentz-violating extension of QED, showing that gauge symmetry conditions mirror those of standard QED and that fermion sector terms can induce photon sector Lorentz violation.

Contribution

It derives gauge invariance conditions for a dimension-5 Lorentz-violating QED and demonstrates radiative induction of Lorentz-violating terms in the photon sector from fermion sector modifications.

Findings

Gauge invariance conditions are identical to standard QED.

One-loop two and three point functions are computed.

Fermion sector Lorentz violation induces photon sector Lorentz violation.

Abstract

In this work, we derive the conditions that assure gauge invariance of a non-minimal dimension-5 Lorentz-violating QED. The two and three point functions at one-loop are computed. The gauge Ward identities are checked and the conditions to assure gauge symmetry of this non-minimal framework is found to be the same of the usual QED. Induced terms are also investigated and it is shown that the non-minimal Lorentz-violating $a^{(5)}_F$-term of the fermion sector can induce radiatively a non-minimal Lorentz-violating term in the photon sector.