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An
evolution equation approach to the Klein–Gordon operator on
curved spacetime
Jan Dereziński and Daniel Siemssen |
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Vol. 1 (2019), No. 2, 215–261
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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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Authors |
| Jan Dereziński | |
| Department of Mathematical Methods
in Physics Faculty of Physics University of Warsaw Warsaw Poland |
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| Daniel Siemssen | |
| Department of Mathematics and
Informatics University of Wuppertal Wuppertal Germany |
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