Derivations of the Moyal Algebra and Noncommutative Gauge Theories
The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital al...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149248 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Derivations of the Moyal Algebra and Noncommutative Gauge Theories / Jean-Christophe Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-149248 |
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Wallet, Jean-Christophe 2019-02-19T19:20:55Z 2019-02-19T19:20:55Z 2009 Derivations of the Moyal Algebra and Noncommutative Gauge Theories / Jean-Christophe Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81T75; 81T13 https://nasplib.isofts.kiev.ua/handle/123456789/149248 The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of Z₂-graded unital involutive algebras. We show, in the case of the Moyal algebra or some related Z₂-graded version of it, that the derivation based differential calculus is a suitable framework to construct Yang-Mills-Higgs type models on Moyal (or related) algebras, the covariant coordinates having in particular a natural interpretation as Higgs fields. We also exhibit, in one situation, a link between the renormalisable NC φ4-model with harmonic term and a gauge theory model. Some possible consequences of this are briefly discussed. This paper is a contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 19–22, 2008, Prague, Czech Republic). It is a pleasure to thank the organisers of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries for their kind invitation. Most of the results presented in this paper have been obtained from various collaborations with E. Cagnache, A. de Goursac and T. Masson. Fruitful discussions with M. Dubois-Violette and J. Madore are gratefully acknowledged. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Derivations of the Moyal Algebra and Noncommutative Gauge Theories Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories |
| spellingShingle |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories Wallet, Jean-Christophe |
| title_short |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories |
| title_full |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories |
| title_fullStr |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories |
| title_full_unstemmed |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories |
| title_sort |
derivations of the moyal algebra and noncommutative gauge theories |
| author |
Wallet, Jean-Christophe |
| author_facet |
Wallet, Jean-Christophe |
| publishDate |
2009 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of Z₂-graded unital involutive algebras. We show, in the case of the Moyal algebra or some related Z₂-graded version of it, that the derivation based differential calculus is a suitable framework to construct Yang-Mills-Higgs type models on Moyal (or related) algebras, the covariant coordinates having in particular a natural interpretation as Higgs fields. We also exhibit, in one situation, a link between the renormalisable NC φ4-model with harmonic term and a gauge theory model. Some possible consequences of this are briefly discussed.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149248 |
| citation_txt |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories / Jean-Christophe Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 52 назв. — англ. |
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