Field Theory on Curved Noncommutative Spacetimes
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 associ...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146363 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862548636117762048 |
|---|---|
| author | Schenkel, A. Uhlemann, C.F. |
| author_facet | Schenkel, A. Uhlemann, C.F. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-11-25T20:31:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146363 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:31:25Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schenkel, A. Uhlemann, C.F. 2019-02-09T09:42:23Z 2019-02-09T09:42:23Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 81T75; 83C65; 53D55 DOI:10.3842/SIGMA.2010.061 https://nasplib.isofts.kiev.ua/handle/123456789/146363 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Field Theory on Curved Noncommutative Spacetimes Article published earlier |
| spellingShingle | Field Theory on Curved Noncommutative Spacetimes Schenkel, A. Uhlemann, C.F. |
| title | Field Theory on Curved Noncommutative Spacetimes |
| title_full | Field Theory on Curved Noncommutative Spacetimes |
| title_fullStr | Field Theory on Curved Noncommutative Spacetimes |
| title_full_unstemmed | Field Theory on Curved Noncommutative Spacetimes |
| title_short | Field Theory on Curved Noncommutative Spacetimes |
| title_sort | field theory on curved noncommutative spacetimes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146363 |
| work_keys_str_mv | AT schenkela fieldtheoryoncurvednoncommutativespacetimes AT uhlemanncf fieldtheoryoncurvednoncommutativespacetimes |