The axial anomaly, dimensional regularization and Lorentz-violating QED

Abstract

In order to treat loops in the Lorentz-violating QED model, we present a derivation of the QED axial anomaly that specifically highlights the infrared origin of the effect. This is done using dimensional regularization while treating ${\gamma }_5$ as a spectator. This enables us to revisit aspects in the fermionic sector of Lorentz-violating QED which have analogous structure to the axial anomaly. In particular, it is shown that both the Chern-Simons and photon mass operators are not induced in the one loop effective action. At lowest order in the Lorentz-violating parameter, we can define a non-relativistic potential that captures the effects of vacuum polarization. This leads to a Zeeman-like effect in vacuum which lifts the two-fold degeneracy of the hydrogen atom S-orbitals.

18 pages, 3 figures; References added, Minor change in the abstract, Improved introduction to better highlight the main results

References in corpus (10)

• Preferred-Frame and CP-Violation Tests with Polarized Electrons
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• Modelling gravity on a hyper-cubic lattice
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Cited by in corpus (2)

• Traces of Lorentz symmetry breaking in a Hydrogen atom at ground state
• Quantum gravity corrections to gauge theories with a cutoff regularization