Fermion effective dispersion relation for z=2 Lifshitz QED

TL;DR

This paper investigates the effects of Lorentz symmetry violation in a z=2 Lifshitz extension of QED, revealing unique regularization properties and analyzing corrections to photon mass and fermion dispersion relations.

Contribution

It introduces a novel regularization approach for Lifshitz QED and examines quantum corrections, highlighting the model's consistency and unique features.

Findings

Loop integrals are finite even in three spatial dimensions.

Photon mass corrections vanish, indicating consistency.

Fermion dispersion relations receive IR-divergence-free corrections.

Abstract

We study consequences of Lorentz symmetry violation in a z=2 Lifshitz extension of QED in 3+1 dimensions, and we discuss non-trivial effects of quantization. Because of the specific power of space momentum in propagators of the model, dimensional regularization leads to an unusual interpretation of loop integrals, which are finite even when the space dimension goes to the integer 3. We check the consistency of the approach by calculating the (vanishing) corrections to the photon mass and the IR-divergence-free corrections to the dispersion relation for massless fermions.