One-loop corrections to the photon propagator in the curved-space QED

TL;DR

This paper computes one-loop quantum corrections to the photon propagator in curved spacetime QED, deriving effective actions and beta-functions relevant for high-energy physics and cosmological applications.

Contribution

It provides a covariant local effective action for photon corrections in curved space and connects conformal anomaly and heat kernel methods for different energy regimes.

Findings

Derived the exact one-loop beta-function for electric charge.

Presented a covariant local effective action for photon corrections.

Explored massless and large mass limits in quantum corrections.

Abstract

We calculate and discuss the one-loop corrections to the photon sector of QED interacting to a background gravitational field. At high energies the fermion field can be taken as massless and the quantum terms can be obtained by integrating conformal anomaly. We present a covariant local expression for the corresponding effective action, similar to the one obtained earlier for the gravitational sector. At the moderate energies the quantum terms can be obtained through the heat kernel method. In this way we derive the exact one-loop beta-function for the electric charge in the momentum subtraction scheme and explore both massless and large mass limits. The relation between the two approaches is shown and the difference discussed in view of the possible applications to cosmology and astrophysics.