Renormalization of Very Special Relativity gauge theories

Abstract

Abstract Mandelstam-Leibbrandt (ML) regularization of Very Special Relativity (VSR) amplitudes in momentum space depends on two fixed null vectors n μ , n ¯ μ $$ {\overline{n}}_{\mu } $$ besides external momenta. ML is known to preserve gauge invariance and naive power counting. The second null vector n ¯ μ $$ {\overline{n}}_{\mu } $$ destroys the Sim(2) symmetry of the VSR model. We devise a systematic procedure to take the n ¯ μ $$ {\overline{n}}_{\mu } $$ → 0 limit to recover the lost Sim(2) symmetry. The procedure produces Sim(2) and gauge invariant loop amplitudes. We show how to use this method to remove unphysical terms from the Non Relativistic Potential of Very Special Relativity Quantum Electrodynamics (VSR QED) with a massive photon. Then we compute the one loop renormalization of VSR QED. Finally we derive the anomalous magnetic moment of the electron, modified by neutrino and photon mass; and comments on the phenomenological implications.

Keywords

• Renormalization and Regularization
• Violation of Lorentz and/or CPT Symmetry
• Space-Time Symmetries