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Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

Ohl, Thorsten; Schenkel, Alexander

Authors

Thorsten Ohl



Abstract

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compute the corresponding equation of motion operators. The Green's operators and the fundamental solution of the deformed equation of motion are obtained in terms of formal power series. It is shown that, using the deformed fundamental solution, we can define deformed *-algebras of field observables, which in general depend on the spacetime deformation parameter. This dependence is absent in the special case of Killing deformations, which include in particular the Moyal-Weyl deformation of the Minkowski spacetime.

Citation

Ohl, T., & Schenkel, A. (2010). Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes. General Relativity and Gravitation, 42(12), 2785–2798. https://doi.org/10.1007/s10714-010-1016-2

Journal Article Type Article
Acceptance Date May 16, 2010
Online Publication Date May 30, 2010
Publication Date May 30, 2010
Deposit Date Aug 22, 2019
Publicly Available Date Jan 22, 2020
Journal General Relativity and Gravitation
Print ISSN 0001-7701
Electronic ISSN 1572-9532
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 42
Issue 12
Pages 2785–2798
DOI https://doi.org/10.1007/s10714-010-1016-2
Keywords High Energy Physics - Theory; General Relativity and Quantum Cosmology; Mathematical Physics
Public URL https://nottingham-repository.worktribe.com/output/2460592
Publisher URL https://link.springer.com/article/10.1007%2Fs10714-010-1016-2