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Abstract
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We develop a theory of the Klein–Gordon equation on curved spacetimes. Our
main tool is the method of (nonautonomous) evolution equations on Hilbert
spaces. This approach allows us to treat low regularity of the metric, of
the electromagnetic potential and of the scalar potential. Our main goal
is a construction of various kinds of propagators needed in quantum field
theory.
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Keywords
Klein–Gordon equation, Klein–Gordon operator, propagator,
evolution equation, quantum field theory, quantum field
theory in curved spacetimes
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Mathematical Subject Classification 2010
Primary: 35L05, 47D06
Secondary: 58J45, 81Q10, 81T20
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Milestones
Received: 16 October 2018
Revised: 8 February 2019
Accepted: 6 March 2019
Published: 20 April 2019
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