Radiatively Induced Lorentz and Gauge Symmetry Violation in Electrodynamics with Varying alpha

TL;DR

This paper explores how a time-varying fine structure constant can induce Lorentz and gauge symmetry violations in electrodynamics, revealing potential instabilities at second order due to vacuum polarization effects.

Contribution

It demonstrates that in the minimal theory of varying alpha, no gauge-violating terms appear at lowest order, but second-order effects can lead to Lorentz-violating instabilities.

Findings

No gauge-violating terms at lowest order in minimal theory

Second-order vacuum polarization induces Lorentz-violating instability

Photon mass squared becomes negative, indicating instability

Abstract

A time-varying fine structure constant alpha(t) could give rise to Lorentz- and CPT-violating changes to the vacuum polarization, which would affect photon propagation. Such changes to the effective action can violate gauge invariance, but they are otherwise permitted. However, in the minimal theory of varying alpha, no such terms are generated at lowest order. At second order, vacuum polarization can generate an instability--a Lorentz-violating analogue of a negative photon mass squared -m^2 proportional to alpha [(d alpha/dt) / alpha]^2 log (Lambda^2), where Lambda is the cutoff for the low-energy effective theory.