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We develop a theory of the Klein-Gordon equation on curved spacetimes. Ourmain tool is the method of (non-autonomous) evolution equations on Hilbertspaces. This approach allows us to treat low regularity of the metric, of theelectromagnetic potential and of the scalar potential. Our main goal is aconstruction of various kinds of propagators needed in quantum field theory.

An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime