QFT on homothetic Killing twist deformed curved spacetimes

Schenkel, Alexander

Abstract

We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel'd twist constructed from a Killing and a homothetic Killing vector field. In contrast to deformations solely by Killing vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of motion and Green's operators are deformed. We show that there is a *-algebra isomorphism between the QFT on the deformed and the formal power series extension of the QFT on the undeformed spacetime. We study the convergent implementation of our deformations for toy-models. For these models it is found that there is a *-isomorphism between the deformed Weyl algebra and a reduced undeformed Weyl algebra, where certain strongly localized observables are excluded. Thus, our models realize the intuitive physical picture that noncommutative geometry prevents arbitrary localization in spacetime.

Citation

Schenkel, A. (2011). QFT on homothetic Killing twist deformed curved spacetimes. General Relativity and Gravitation, 43, 2605–2630. https://doi.org/10.1007/s10714-011-1184-8

• Journal Article Type: Article
• Acceptance Date: Apr 14, 2014
• Online Publication Date: Apr 23, 2011
• Publication Date: 2011-10
• Deposit Date: Aug 22, 2019
• Publicly Available Date: Mar 29, 2020
• Journal: General Relativity and Gravitation
• Print ISSN: 0001-7701
• Electronic ISSN: 1572-9532
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Pages: 2605–2630
• DOI: https://doi.org/10.1007/s10714-011-1184-8
• Keywords: Mathematical Physics; General Relativity and Quantum Cosmology; High Energy Physics - Theory
• Public URL: https://nottingham-repository.worktribe.com/output/2460586
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10714-011-1184-8