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Field Theory on Curved Noncommutative Spacetimes

Please always quote using this URN: urn:nbn:de:bvb:20-opus-68648
  • 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 curvedWe 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.show moreshow less

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Metadaten
Author: Alexander Schenkel, Christoph F. Uhlemann
URN:urn:nbn:de:bvb:20-opus-68648
Document Type:Journal article
Faculties:Fakultät für Physik und Astronomie / Institut für Theoretische Physik und Astrophysik
Language:English
Year of Completion:2010
Source:In: Symmetry, Integrability and Geometry: Methods and Applications (2010) 6, 061 DOI: 10.3842/SIGMA.2010.061
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
GND Keyword:Physik
Tag:Drinfel’d twists; deformation quantization; field theory on curved spacetimes; noncommutative field theory
Release Date:2012/11/12
Licence (German):License LogoCC BY-NC-SA: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell, Weitergabe unter gleichen Bedingungen