Extracting Hadamard Coefficients from Green's Operators

Abstract

We develop a formula for the diagonal values of the Hadamard coefficients associated to a normally hyperbolic operator on a globally hyperbolic spacetime in terms of the advanced and retarded Green's operators. We develop a local formula as well as formulae for integrals over (parts of) the diagonal. Furthermore, we develop analogues of the Hadamard expansion for powers of the advanced/retarded Green's operators and an analogue of a resolvent.

arXiv commentThis is the Author's Ph. D. thesis (with minor typo corrections), advised by Prof. Matthias Lesch and unofficially also advised by Dr. Koen van den Dungen. A shorter and more easily readable version of the part on additional expansions is in the making