The regularized phase space path integral measure for Maxwell fields coupled to background gravity (Q809430)

The authors consider a quantized Maxwell field in an external gravitational field. There are two ways to construct the phase space path integral: First go to the classical Hamiltonian and then covariantly quantize it or: First quantize the configuration space action and then go to the Hamiltonian version. It is shown that both approaches lead to the same phase space path integral up to redefinition of the external gravitational momentum. Then the Pauli-Vilars action and an Einstein invariant mass term are constructed. As a consequence Einstein anomalies are absent.