One-loop Euler-Heisenberg action in Lorentz-violating QED revisited

TL;DR

The paper addresses the one-loop Lorentz-violating Euler–Heisenberg action in a spinor QED modified by a CPT-even mass-term $H_{\mu\nu}$. It derives the LV EH action to first order in $H_{\mu\nu}$ using the proper-time method and confirms the result with a Feynman-diagram calculation, showing the action depends only on odd powers of $F_{\mu\nu}$ and is UV finite. The authors demonstrate a precise agreement between the proper-time derivation and the three-point-function computation, and discuss extensions to other LV operators and phenomenology.

Abstract

We discuss applications of the proper-time method in a Lorentz-violating extension of QED characterized by the modification of the mass sector through the addition of the term proportional to the antisymmetric tensor $H_{μν}$. Unlike other LV extensions of QED, in our case the one-loop Euler-Heisenberg-like action turns out to include only odd degrees of the stress tensor $F_{μν}$. Our result is shown to be UV finite, and it is confirmed using the Feynman diagrams framework.