One-loop renormalization of quantum electrodynamics in curved spacetime

Abstract

In this paper we discuss the renormalizability of quantum electrodynamics (QED) in a general curved spacetime. A generating functional is introduced and position-space Feynman rules are obtained. Functional techniques are used to show that a form of Ward's identity can be derived in curved spacetime. A local momentum representation for the scalar and vector propagators is introduced. The one-loop diagrams for the electron and photon self-energy are computed and it is shown that there are no divergences that are not present in flat space. It is shown that this latter result depends crucially on the gauge invariance of the theory and is not merely a trivial consequence of renormalizability of QED in flat spacetime.