On the effective action of the vacuum photon splitting in Lorentz-violating QED

TL;DR

This paper investigates the possibility of photon triple splitting in Lorentz-violating QED and finds that, at leading order, such an effective action cannot be explicitly derived using the derivative expansion method.

Contribution

It provides a detailed analysis showing the non-existence of a nonzero photon triple splitting effective action at leading order in Lorentz-violating QED.

Findings

Photon triple splitting effective action is zero at leading order.

Derivative expansion method does not yield nonzero results for this process.

Highlights limitations of current methods in Lorentz-violating QED.

Abstract

We consider one-loop radiative corrections from Lorentz- and CPT- violating extended QED to address the specific problem of finding explicitly an effective action describing amplitude of photon triple splitting. We show that it is not possible to find a nonzero photon triple splitting effective action, at least by using the derivative expansion method (at zero external momenta), up to leading order in the Lorentz- and CPT- violating parameter.