%0 Journal Article
%T Field Theory on Curved Noncommutative Spacetimes
%A Alexander Schenkel
%A Christoph F. Uhlemann
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2010
%I National Academy of Science of Ukraine
%X 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.
%K noncommutative field theory
%K Drinfel'd twists
%K deformation quantization
%K field theory on curved spacetimes
%U http://dx.doi.org/10.3842/SIGMA.2010.061