One-loop calculations in Lorentz-breaking theories and proper-time method

TL;DR

This paper applies the proper-time method to compute one-loop effective actions in minimal Lorentz-violating QED extensions, providing new explicit results for models involving axial vectors and tensors.

Contribution

It introduces new calculations of the one-loop Heisenberg-Euler effective action in Lorentz-violating QED models using the proper-time method.

Findings

Explicit one-loop effective actions for Lorentz-violating QED extensions.

New results for models with axial vector and tensor Lorentz violation.

Demonstrates the applicability of the proper-time method in Lorentz-violating theories.

Abstract

We discuss applications of the proper-time method in various minimal Lorentz violating modifications of QED and present new results obtained with its use. Explicitly. we calculate the complete one-loop Heisenberg-Euler effective action involving all orders in $F_{mn}$, for two of the most studied minimal Lorentz-violating extensions of QED, the one characterized by the axial vector $b^m$ and the one involving the second-rank constant tensor $c^{mn}$.