QED on Curved Background and on Manifolds with Boundaries: Unitarity versus Covariance

TL;DR

This paper resolves a conflict between unitarity and covariance in quantum field theory on curved backgrounds by emphasizing the importance of using a covariant measure in the path integral, restoring consistency.

Contribution

It demonstrates that employing a covariant measure in the reduced phase space path integral resolves discrepancies and preserves symmetries in quantum gravity on curved manifolds.

Findings

Covariant measure restores standard path integral results.

Non-covariant measure breaks basic symmetries.

Covariant approach aligns with BRST-invariant boundary conditions.

Abstract

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 non-covariant 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.