On Unitary Evolution in Quantum Field Theory in Curved Spacetime

Details On Unitary Evolution in Quantum Field Theory in Curved Spacetime On Unitary Evolution in Quantum Field Theory in Curved Spacetime

2009-12-03

arxiv.org/abs/0912.0556v2

The Open Nuclear and Particle Physics Journal 4 (2011), 13-20

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX + revtex4; v2: minor improvements and corrections

Scientific paper

10.2174/1874415X01104010013

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.

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