Field Theory on Curved Noncommutative Spacetimes

Symmetry Integrability and Geometry-Methods and Applications

article

Alexander Schenkel¹  Christoph F. Uhlemann¹ 

[1] Institut für Theoretische Physik und Astrophysik

关键词: noncommutative field theory;    Drinfel’d twists;    deformation quantization;    field theory on curved spacetimes;   

DOI  :  10.3842/SIGMA.2010.061

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown