Impossibility of obtaining a CP-violating Euler-Heisenberg effective theory from a viable modification of QED

TL;DR

This paper demonstrates that a CP-violating Euler-Heisenberg effective action cannot be derived from any viable modification of QED, highlighting fundamental limitations in generating such terms within known quantum field theories.

Contribution

It shows that CP-violating terms in the Euler-Heisenberg action are only obtainable from anomalous models, which are not viable extensions of QED.

Findings

CP-violating Euler-Heisenberg terms are linked to vector and axial fermionic bilinears.

Such CP-violating terms cannot be generated from any viable QED modification.

Only anomalous models produce these CP-violating contributions, which are not fundamental theories.

Abstract

In this paper, we examine the CP-violating term of the Euler-Heisenberg action. We focus in the aspects related with the generation of such a term from a QED-like model in terms of the effective action approach. In particular, we show that the generation of the CP-violating term is closely related with both of vector and axial fermionic bilinears. Although, these anomalous models are not a "viable" extension of QED, we argue that the CP-violating term in the photon sector is obtained only from this class of models, and not from any fundamental field theory.