Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level

Abstract

We address the study of gauge invariance in the Standard Model Extension which encompasses all Lorentz-violating terms originated by spontaneous symmetry breaking at the Planck scale. In particular, we fully evaluate Ward identities involving two and three point functions and derive the conditions which assure gauge invariance of the electromagnetic sector of the Standard Model Extension at one-loop. We show that momentum routing invariance is sufficient to fix arbitrary and regularization dependent parameters intrinsic to perturbation theory in the diagrams involved. A scheme which judiciously collects finite but undetermined quantum corrections is employed, a particularly subtle issue in the presence of ${\gamma }_5$ matrices.

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• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations
• ${\gamma }_5$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$
• Lorentz-violating Yang-Mills theory: discussing the Chern-Simons-like term generation
• Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods
• On the Bose symmetry and the left- and right-chiral anomalies
• A step towards a consistent treatment of chiral theories at higher loop order: the abelian case
• Gauge anomalies in Lorentz-violating QED
• Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory
• Advances towards the systematization of calculations with Implicit Regularization
• Infrared Subtleties and Chiral Vertices at NLO: An Implicit Regularization Analysis
• Do anomalies break the momentum routing invariance?