Vol. 1, No. 2, 2019

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An evolution equation approach to the Klein–Gordon operator on curved spacetime

Jan Dereziński and Daniel Siemssen

Vol. 1 (2019), No. 2, 215–261

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.

Klein–Gordon equation, Klein–Gordon operator, propagator, evolution equation, quantum field theory, quantum field theory in curved spacetimes
Mathematical Subject Classification 2010
Primary: 35L05, 47D06
Secondary: 58J45, 81Q10, 81T20
Received: 16 October 2018
Revised: 8 February 2019
Accepted: 6 March 2019
Published: 20 April 2019
Jan Dereziński
Department of Mathematical Methods in Physics
Faculty of Physics
University of Warsaw
Daniel Siemssen
Department of Mathematics and Informatics
University of Wuppertal