Generation of higher derivatives operators and electromagnetic wave propagation in a Lorentz-violation scenario

TL;DR

This paper investigates how Lorentz-violating backgrounds induce higher-derivative operators in the photon effective action and examines their impact on electromagnetic wave propagation in a strong magnetic field, finding no detectable effects.

Contribution

It provides a detailed one-loop calculation of higher-derivative corrections from Lorentz violation and analyzes their influence on electromagnetic wave propagation, revealing cancellations that prevent detection.

Findings

Lorentz-violating corrections cancel out in Maxwell's equations.

No observable effects of Lorentz violation in electromagnetic wave propagation under studied conditions.

Higher-derivative operators do not lead to measurable deviations in the presence of a strong magnetic field.

Abstract

We study the perturbative generation of higher-derivative operators as corrections to the photon effective action, which are originated from a Lorentz violation background. Such corrections are obtained, at one-loop order, through the proper-time method, using the zeta function regularization. We focus over the lowest order corrections and investigate their influence in the propagation of electromagnetic waves through the vacuum, in the presence of a strong, constant magnetic field. This is a setting of experimental relevance, since it bases active efforts to measure non linear electromagnetic effects. After surprising cancellations of Lorentz violating corrections to the Maxwell's equation, we show that no effects of the kind of Lorentz violation we consider can be detected in such a context.