Field Theory on Curved Noncommutative Spacetimes

Schenkel, Alexander; F. Uhlemann, Christoph

Abstract

We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by using (Abelian) Drinfel'd twists and the associated *-products and *-differential geometry. In particular, we allow for position dependent noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation. We construct action functionals for real scalar fields on noncommutative curved spacetimes, and derive the corresponding deformed wave equations. We provide explicit examples of deformed Klein-Gordon operators for noncommutative Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve the noncommutative Einstein equations. We study the construction of deformed Green's functions and provide a diagrammatic approach for their perturbative calculation. The leading noncommutative corrections to the Green's functions for our examples are derived.

Citation

Schenkel, A., & F. Uhlemann, C. (2010). Field Theory on Curved Noncommutative Spacetimes. Symmetry, Integrability and Geometry: Methods and Applications, 6, Article 061. https://doi.org/10.3842/SIGMA.2010.061

• Journal Article Type: Article
• Acceptance Date: Jul 14, 2010
• Online Publication Date: Aug 3, 2010
• Publication Date: Aug 3, 2010
• Deposit Date: Aug 22, 2019
• Electronic ISSN: 1815-0659
• Peer Reviewed: Peer Reviewed
• Volume: 6
• Article Number: 061
• DOI: https://doi.org/10.3842/SIGMA.2010.061
• Keywords: High Energy Physics - Theory; General Relativity and Quantum Cosmology; Mathematical Physics
• Public URL: https://nottingham-repository.worktribe.com/output/2460600
• Publisher URL: http://www.emis.de/journals/SIGMA/2010/061/