The regularized phase space path integral measure for Maxwell fields coupled to background gravity

Abstract

In order to construct the phase space path integral for the Einstein-Maxwell system with the gravitational field kept external, one can use covariant quantization and gauge fix the U(1) symmetry before or after passing to the action in Hamiltonian form. In this paper we show that both approaches lead to the same phase space path integral up to redefinition of the external gravitational momentum. We then construct the Pauli-Villars action, which regularizes one-loop diagrams, and construct an Einstein invariant mass term. As a consequence Einstein anomalies are absent. We cast the gauge fixing and the ghost action in the usual pq̇ − λ α H α form by using a noncoordinate basis.