Gauge Independent Quantum Gravitational Corrections to Maxwell's Equation

TL;DR

This paper derives a gauge-independent, quantum gravitational correction to Maxwell's equations, ensuring the effective field remains real, causal, and consistent despite gauge-dependent vacuum polarization.

Contribution

It presents a method to cancel gauge dependence in quantum gravitational corrections to Maxwell's equations, resulting in a gauge-independent effective field equation.

Findings

Gauge dependence in vacuum polarization is canceled by source and observer contributions.

The resulting effective field equation is gauge independent, real, and causal.

The correction can be used similarly to classical Maxwell's equations.

Abstract

We consider quantum gravitational corrections to Maxwell's equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation.