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Feynman propagators on static spacetimes

Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland

E-mail Address: jan.derezinski@fuw.edu.pl

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and

Daniel Siemssen

Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland

Department of Mathematics and Informatics, University of Wuppertal, Gaußstraße 20, 42119, Wuppertal, Germany

E-mail Address: siemssen@uni-wuppertal.de

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https://doi.org/10.1142/S0129055X1850006XCited by:21 (Source: Crossref)

Abstract

We consider the Klein–Gordon equation on a static spacetime and minimally coupled to a static electromagnetic potential. We show that it is essentially self-adjoint on $C_{c}^{\infty}$ $C_{c}^{\infty}$ . We discuss various distinguished inverses and bisolutions of the Klein–Gordon operator, focusing on the so-called Feynman propagator. We show that the Feynman propagator can be considered the boundary value of the resolvent of the Klein–Gordon operator, in the spirit of the limiting absorption principle known from the theory of Schrödinger operators. We also show that the Feynman propagator is the limit of the inverse of the Wick rotated Klein–Gordon operator.

Keywords:

AMSC: 35L05, 47D06, 58J45, 81Q10, 81T20

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