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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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149248 |
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irk-123456789-1492482019-02-20T01:26:53Z Derivations of the Moyal Algebra and Noncommutative Gauge Theories Wallet, Jean-Christophe 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149248 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Wallet, Jean-Christophe |
| spellingShingle |
Wallet, Jean-Christophe Derivations of the Moyal Algebra and Noncommutative Gauge Theories Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Wallet, Jean-Christophe |
| author_sort |
Wallet, Jean-Christophe |
| title |
Derivations of the Moyal Algebra and Noncommutative Gauge Theories |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT walletjeanchristophe derivationsofthemoyalalgebraandnoncommutativegaugetheories |
| first_indexed |
2023-05-20T17:32:33Z |
| last_indexed |
2023-05-20T17:32:33Z |
| _version_ |
1796153531189690368 |