Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level

TL;DR

This paper investigates gauge invariance in the Standard Model Extension with Lorentz-violating terms, demonstrating that momentum routing invariance ensures gauge invariance at one-loop and addressing regularization ambiguities.

Contribution

It establishes that momentum routing invariance suffices to fix regularization-dependent parameters in one-loop calculations of the extended QED, ensuring gauge invariance.

Findings

Momentum routing invariance guarantees gauge invariance at one-loop.

A scheme for handling finite quantum corrections with $\,\gamma_5$ matrices.

Conditions derived for gauge invariance in Lorentz-violating QED.

Abstract

We address the study of gauge invariance in the Standard Model Extension which encompasses all Lorentz-violating terms originated by spontaneous symmetry breaking at the Planck scale. In particular, we fully evaluate Ward identities involving two and three point functions and derive the conditions which assure gauge invariance of the electromagnetic sector of the Standard Model Extension at one-loop. We show that momentum routing invariance is sufficient to fix arbitrary and regularization dependent parameters intrinsic to perturbation theory in the diagrams involved. A scheme which judiciously collects finite but undetermined quantum corrections is employed, a particularly subtle issue in the presence of $\gamma_5$ matrices.