On Unitary Evolution in Quantum Field Theory in Curved Spacetime

TL;DR

This paper examines the unitarity of quantum evolution in curved spacetime using the general boundary formulation, finding that it is generally unitary under certain conditions in Klein-Gordon theory.

Contribution

It demonstrates that quantum evolution between hypersurfaces in curved spacetime is typically unitary, extending to certain timelike hypersurfaces, using the Schrödinger representation and path integrals.

Findings

Unitarity holds for pairs of Cauchy hypersurfaces.

Unitarity extends to some timelike hypersurfaces.

Classical solutions correspondence ensures unitarity.

Abstract

We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that maps the state space associated with one hypersurface to the state space associated with the other hypersurface. Working in Klein-Gordon theory, we find that such an evolution is generically unitary given a one-to-one correspondence between classical solutions in neighborhoods of the respective hypersurfaces. This covers the case of pairs of Cauchy hypersurfaces, but also certain cases where hypersurfaces are timelike. The tools we use are the Schroedinger representation and the Feynman path integral.