QED with minimal and nonminimal couplings: on the quantum generation of Lorentz violating terms in the pure photon sector

TL;DR

This paper investigates how adding a nonminimal Lorentz-violating interaction to QED can radiatively generate CPT-even and odd Lorentz-breaking terms in the photon sector, emphasizing gauge invariance's role at one-loop order.

Contribution

It demonstrates the radiative generation of Lorentz-violating terms in the photon sector from a nonminimal coupling in QED, highlighting gauge invariance's importance and providing a general form of breaking terms.

Findings

Lorentz-violating terms are generated radiatively in the photon sector.

Gauge invariance constrains the form of these Lorentz-violating terms.

The structure of breaking terms can be organized as a power series in the small parameter $b_\mu$.

Abstract

We consider an effective model formed by usual QED (minimal coupling) with the addition of a nonminimal Lorentz violating interaction (proportional to a fixed 4-vector $b_\mu$) which may radiatively generate both CPT even and odd terms in the pure gauge sector. We show that gauge invariance from usual QED, considered as a limit of the model for $b_\mu \rightarrow 0$, plays an important role in the discussion of the radiatively induced Lorentz violating terms at one-loop order. Moreover, despite the nonrenormalizability of the (effective) model preventing us from readily extending our discussion to higher orders, it is still possible to display the general form of the breaking terms of the photon sector in the on shell limit organized in powers of $b_\mu$ which in turn can be considered as a small expansion parameter.