A Deformation Quantization for Non-Flat Spacetimes and Applications to QFT

We provide a deformation quantization, in the sense of Rieffel, for \textit{all} globally hyperbolic spacetimes with a Poisson structure. The Poisson structures have to satisfy Fedosov type requirements in order for the deformed product to be associative. We apply the novel deformation to quantum fi...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Author: Much, Albert
Format: Article
Language:English
Subjects:
Deformation
Equivalence principle
Measurement
Quantum theory
Spacetime
Online Access:Get full text
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Summary:We provide a deformation quantization, in the sense of Rieffel, for \textit{all} globally hyperbolic spacetimes with a Poisson structure. The Poisson structures have to satisfy Fedosov type requirements in order for the deformed product to be associative. We apply the novel deformation to quantum field theories and their respective states and we prove that the deformed state (i.e.\ a state in non-commutative spacetime) has a singularity structure resembling Minkowski, i.e.\ is \textit{Hadamard}, if the undeformed state is Hadamard. This proves that the Hadamard condition, and hence the quantum field theoretical implementation of the equivalence principle is a general concept that holds in spacetimes with quantum features (i.e. a non-commutative spacetime).
ISSN:2331-8422
DOI:10.48550/arxiv.2109.14507