One-loop corrections to the photon propagator in curved-space QED
Bruno Gonçalves, Guilherme de Berredo-Peixoto, Ilya L. Shapiro · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 2009
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 $\ensuremath{\beta}$ 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.