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Field Theory on Curved Noncommutative Spacetimes
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Field Theory on Curved Noncommutative Spacetimes
Інший ID:
2010 Mathematics Subject Classification: 81T75; 83C65; 53D55
DOI:10.3842/SIGMA.2010.061
DOI:10.3842/SIGMA.2010.061
Посилання:
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.
Підтримка:
This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
We thank Thorsten Ohl for comments and discussions on this work. AS also thanks the Alessandria Mathematical Physics Group, in particular Paolo Aschieri, and the Vienna Mathematical Physics Group, in particular Claudio Dappiaggi and Gandalf Lechner, for discussions and comments. CFU is supported by the German National Academic Foundation (Studienstiftung des deutschen Volkes). AS and CFU are supported by Deutsche Forschungsgemeinschaft through the Research Training Group GRK 1147 Theoretical Astrophysics and Particle Physics.
Дата:
2010
Переглядів:
486
Завантажень:
250
Анотація:
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.
