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

September 12, 2017

We develop a theory of the Klein-Gordon equation on curved spacetimes. Our
main tool is the method of (non-autonomous) 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.

open access link

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@article{Derezinski:2017hvk,
author = "Dereziński, Jan and Siemssen, Daniel",
title = "{An Evolution Equation Approach to the Klein-Gordon
Operator on Curved Spacetime}",
journal = "Analysis",
volume = "1",
year = "2019",
pages = "215-261",
doi = "10.2140/paa.2019.1.215",
eprint = "1709.03911",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1709.03911;%%"
}

Keywords:

Klein-Gordon, evolution operator