All orders renormalizability of a Lorentz and CPT violating quantum electrodynamics

TL;DR

This paper proves that a Lorentz and CPT violating extension of quantum electrodynamics remains renormalizable at all orders, provided certain symmetry conditions are met, ensuring its theoretical consistency.

Contribution

It demonstrates the all-order renormalizability of a Lorentz and CPT violating QED extension using algebraic renormalization, identifying conditions to avoid gauge anomalies.

Findings

New structures potentially causing gauge anomalies are identified.

Anomaly absence is ensured by invariance under C and PT transformations.

Full renormalizability is confirmed under these symmetry conditions.

Abstract

Renormalizability of the (minimal) single-fermion QED extension is investigated at all orders of perturbation theory in the framework of algebraic renormalization, a regularization-independent method. Relative to the standard QED, new structures that could lead to gauge anomalies are identified. Nevertheless, even if the anomaly coefficients fail to vanish in the general case, they shall be absent provided we require invariance of the action under C and/or PT transformations. Stability is also verified in this case, hence full renormalizability is attained.