On the CPT-even Lorentz-breaking extension of the QED

TL;DR

This paper investigates the effects of CPT-even Lorentz-violating terms in quantum electrodynamics, focusing on the fermion sector and the generation of aether-like terms for the gauge field, with implications for renormalization.

Contribution

It introduces a parametrization of the Lorentz-breaking tensor and computes the perturbative generation of gauge field terms up to third order, analyzing renormalization schemes.

Findings

Generated aether-like gauge terms perturbatively up to third order.

Analyzed renormalization schemes for different tensor configurations.

Provided insights into the impact of Lorentz violation on QED.

Abstract

In this paper, we describe the quantum electrodynamics added by Lorentz-violating CPT-even terms in the context of the standard model extension. We focus our attention on the fermion sector, represented by the CPT-even symmetric Lorentz-breaking tensor $c_{\mu\nu}$. We adopt a generic form that parametrizes the components of $c_{\mu\nu}$ in terms of one four-vector, namely, $c_{\mu\nu}=u_\mu u_\nu - \zeta \frac{u^2}{4}g_{\mu\nu}$. We then generate perturbatively, up to the third order in this tensor, the aether-like term for the gauge field. Finally, we discuss the renormalization scheme for the gauge propagator, by taking into account $c_{\mu\nu}$ traceless ($\zeta=1)$ and, trivially, $c_{\mu\nu}=u_\mu u_\nu$ ($\zeta=0$).