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

Ohl, Thorsten; Schenkel, Alexander

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.

• 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
• Journal: General Relativity and Gravitation
• Print ISSN: 0001-7701
• 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