Unitarity of Maxwell theory on curved spacetimes in the covariant formalism

Understand

Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism.

• For gauge theories, these two approaches have produced conflicting results, leading to the question of whether the canonical approach is covariant, and whether the path integral approach is unitary.
• We show the unitarity of the covariant U(1) Maxwell theory, defined via the Wick rotation of a Euclidean path integral.
• We begin by gauge-fixing the path integral, taking care with zero modes, large gauge transformations, and nontrivial bundles.