Quantum Effects of a Spacetime Varying alpha on the Propagation of Electrically Charged Fermions

TL;DR

This paper investigates how a spacetime-varying fine structure constant alpha can induce quantum corrections leading to Lorentz-violating effects in charged fermions, with implications for gauge invariance and quantum electrodynamics.

Contribution

It demonstrates that a varying alpha induces specific Lorentz-violating operators in the SME through one-loop quantum corrections, revealing new effects on gauge invariance.

Findings

Generation of g^(lambda mu nu) and c^(mu nu) Lorentz-violating terms

Radiatively induced violation of gauge invariance

Dependence of corrections on the gradient of alpha

Abstract

A spacetime-varying fine structure constant alpha(x^mu) could generate quantum corrections in some of the coefficients of the Lorentz-violating standard model extension (SME) associated with electrically charged fermions. The quantum corrections depend on d_mu alpha, the spacetime gradient of the fine structure constant. Lorentz-violating operators involving fermions arise from the one-loop corrections to the quantum electrodynamics (QED) vertex function and fermion self-energy. Both g^(lambda mu nu) and c^(mu nu) terms are generated, at O(d_mu alpha) and O[(d_mu alpha)^2], respectively. The g^(lambda mu nu) terms so generated are different in the vertex and self-energy, which represents a radiatively induced violation of gauge invariance.