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Mathematics > Analysis of PDEs
Title: On microlocalisation and the construction of Feynman Propagators for normally hyperbolic operators
(Submitted on 17 Dec 2020 (v1), last revised 28 Mar 2024 (this version, v3))
Abstract: This article gives global microlocalisation constructions for normally hyperbolic operators on a vector bundle over a globally hyperbolic spacetime in geometric terms. As an application, this is used to generalise the Duistermaat-H\"{o}rmander construction of Feynman propagators, therefore incorporating the most important non-scalar geometric operators. It is shown that for normally hyperbolic operators that are selfadjoint with respect to a hermitian bundle metric, the Feynman propagators can be constructed to satisfy a positivity property that reflects the existence of Hadamard states in quantum field theory on curved spacetimes. We also give a more direct construction of the Feynman propagators for Dirac-type operators on a globally hyperbolic spacetime. Even though the natural bundle metric on spinors is not positive-definite, in this case, we can give a direct microlocal construction of a Feynman propagator that satisfies positivity.
Submission history
From: Onirban Islam [view email][v1] Thu, 17 Dec 2020 17:22:51 GMT (64kb)
[v2] Wed, 7 Dec 2022 13:47:11 GMT (65kb)
[v3] Thu, 28 Mar 2024 09:30:38 GMT (66kb)
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