Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1811-1883 |
| Seitenumfang | 73 |
| Fachzeitschrift | Communications in Analysis and Geometry |
| Jahrgang | 32 |
| Ausgabenummer | 7 |
| Publikationsstatus | Veröffentlicht - 3 Dez. 2024 |
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-Hörmander 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 Diractype 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Statistik und Wahrscheinlichkeit
- Mathematik (insg.)
- Geometrie und Topologie
- Entscheidungswissenschaften (insg.)
- Statistik, Wahrscheinlichkeit und Ungewissheit
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in: Communications in Analysis and Geometry, Jahrgang 32, Nr. 7, 03.12.2024, S. 1811-1883.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On microlocalisation and the construction of Feynman propagators for normally hyperbolic operators
AU - Islam, Onirban
AU - Strohmaier, Alexander
N1 - Publisher Copyright: © 2024 International Press, Inc.. All rights reserved.
PY - 2024/12/3
Y1 - 2024/12/3
N2 - 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-Hörmander 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 Diractype 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.
AB - 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-Hörmander 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 Diractype 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.
UR - http://www.scopus.com/inward/record.url?scp=85214555855&partnerID=8YFLogxK
U2 - 10.4310/CAG.241204020919
DO - 10.4310/CAG.241204020919
M3 - Article
AN - SCOPUS:85214555855
VL - 32
SP - 1811
EP - 1883
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
SN - 1019-8385
IS - 7
ER -