TY  - JOUR
A1  - Schenkel, Alexander
A1  - Uhlemann, Christoph F.
T1  - Field Theory on Curved Noncommutative Spacetimes
N2  - 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.
KW  - Physik
KW  - noncommutative field theory
KW  - Drinfel’d twists
KW  - deformation quantization
KW  - field theory on curved spacetimes
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-68648
ER  -