QED on a curved background and on manifolds with boundaries: Unitarity versus covariance.

Some recent results show that the covariant path integral and the integral over physical degrees of freedom give contradicting results on curved background and on manifolds with boundaries. This looks like a conflict between unitarity and covariance. We argue that this effect is due to the use of noncovariant measure on the space of physical degrees of freedom. Starting with the reduced phase space path integral and using covariant measure throughout computations we recover standard path integral in the Lorentz gauge and the Moss and Poletti BRST-invariant boundary conditions. We also demonstrate by direct calculations that in the approach based on Gaussian path integral on the space of physical degrees of freedom some basic symmetries are broken. PACS: 04.20, 03.50, 11.15 Permanent address: Department of Theoretical Physics, St.Petersburg University, 198904 St.Petersburg, Russia, e.-mail: dvassil @ sph.spb.su