Details
| Original language | English |
|---|---|
| Pages (from-to) | 1811-1883 |
| Number of pages | 73 |
| Journal | Communications in Analysis and Geometry |
| Volume | 32 |
| Issue number | 7 |
| Publication status | Published - 3 Dec 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 subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Geometry and Topology
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Communications in Analysis and Geometry, Vol. 32, No. 7, 03.12.2024, p. 1811-1883.
Research output: Contribution to journal › Article › Research › 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 -