Field Theory on Curved Noncommutative Spacetimes

Details Field Theory on Curved Noncommutative Spacetimes Field Theory on Curved Noncommutative Spacetimes

2010-03-16

arxiv.org/abs/1003.3190v2

SIGMA 6 (2010), 061, 19 pages

Physics

High Energy Physics

High Energy Physics - Theory

SIGMA Special Issue on Noncommutative Spaces and Fields

Scientific paper

10.3842/SIGMA.2010.061

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.

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