No one-loop gauge anomalies for a Lorentz-violating quantum electrodynamics: Evaluation of the three-photon vertex

Abstract

Identification of the diagrams that can lead to gauge anomalies in the (minimal) Lorentz- and $CPT$-violating extension of quantum electrodynamics reveals these are the electron self-energy and vertex correction (related to the Ward-Takahashi identity), the photon self-energy (related to the vacuum polarization tensor transversality), and the three-photon vertex diagrams. All but the latter were explicitly verified to be free of anomalies to first order in loop expansion. Here we provide this remaining evaluation and verify the absence of anomalies in this process.

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• Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
• Remarks on the renormalization properties of Lorentz and CPT violating quantum electrodynamics
• Gauge anomalies in Lorentz-violating QED
• On the anomalies in Lorentz-breaking theories
• Induction of the Lorentz-violating effective actions in quantum electrodynamics