Field Theory on Curved Noncommutative Spacetimes

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Authors: Schenkel, A., Uhlemann, C.F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146363
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Field Theory on Curved Noncommutative Spacetimes / A. Schenkel, C.F. Uhlemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 41 назв. — англ.

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.