A deformation quantization for non-flat spacetimes and applications to QFT
Year: 2024
Type: article
Abstract: We provide a deformation quantization, in the sense of Rieffel, for 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 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).
Author: Albert Much
Institution: Leipzig University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,165
OpenAlex ID: W4399933799