Gravitational Correction to Vacuum Polarization

TL;DR

This paper investigates how a gravitational background influences vacuum polarization, showing that while the speed of light remains unaffected on-shell, off-shell photons experience quantum gravitational corrections.

Contribution

It introduces a method to incorporate gravitational corrections into the Dirac propagator, ensuring the equivalence principle is maintained in quantum electrodynamics.

Findings

Gravitational correction vanishes on the photon mass shell.

Off-shell virtual photons exhibit nontrivial gravitational effects.

Results align with the equivalence principle and recent theoretical studies.

Abstract

We consider the gravitational correction to (electronic) vacuum polarization in the presence of a gravitational background field. The Dirac propagators for the virtual fermions are modified to include the leading gravitational correction (potential term) which corresponds to a coordinate-dependent fermion mass. The mass term is assumed to be uniform over a length scale commensurate with the virtual electron-positron pair. The on-mass shell renormalization condition ensures that the gravitational correction vanishes on the mass shell of the photon, i.e., the speed of light is unaffected by the quantum field theoretical loop correction, in full agreement with the equivalence principle. Nontrivial corrections are obtained for off-shell, virtual photons. We compare our findings to other works on generalized Lorentz transformations and combined quantum-electrodynamic gravitational corrections to the speed of light which have recently appeared in the literature.