Dirac Operators on Noncommutative Curved Spacetimes
We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy. These criteria turn out to be restrictive, but th...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149372 |
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| Цитувати: | Dirac Operators on Noncommutative Curved Spacetimes / A. Schenkel, C.F. Uhlemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 36 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149372 |
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dspace |
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irk-123456789-1493722019-02-22T01:23:39Z Dirac Operators on Noncommutative Curved Spacetimes Schenkel, A. Uhlemann, C.F. We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy. These criteria turn out to be restrictive, but they do not fix a unique construction: two of our operators generally satisfy the axioms, and we provide an explicit example where they are inequivalent. For highly symmetric spacetimes with Drinfeld twists constructed from sufficiently many Killing vector fields, all of our operators coincide. For general noncommutative curved spacetimes we find that demanding formal self-adjointness as an additional condition singles out a preferred choice among our candidates. Based on this noncommutative Dirac operator we construct a quantum field theory of Dirac fields. In the last part we study noncommutative Dirac operators on deformed Minkowski and AdS spacetimes as explicit examples. 2013 Article Dirac Operators on Noncommutative Curved Spacetimes / A. Schenkel, C.F. Uhlemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T75; 81T20; 83C65 DOI: http://dx.doi.org/10.3842/SIGMA.2013.080 http://dspace.nbuv.gov.ua/handle/123456789/149372 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 |
We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy. These criteria turn out to be restrictive, but they do not fix a unique construction: two of our operators generally satisfy the axioms, and we provide an explicit example where they are inequivalent. For highly symmetric spacetimes with Drinfeld twists constructed from sufficiently many Killing vector fields, all of our operators coincide. For general noncommutative curved spacetimes we find that demanding formal self-adjointness as an additional condition singles out a preferred choice among our candidates. Based on this noncommutative Dirac operator we construct a quantum field theory of Dirac fields. In the last part we study noncommutative Dirac operators on deformed Minkowski and AdS spacetimes as explicit examples. |
| format |
Article |
| author |
Schenkel, A. Uhlemann, C.F. |
| spellingShingle |
Schenkel, A. Uhlemann, C.F. Dirac Operators on Noncommutative Curved Spacetimes Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schenkel, A. Uhlemann, C.F. |
| author_sort |
Schenkel, A. |
| title |
Dirac Operators on Noncommutative Curved Spacetimes |
| title_short |
Dirac Operators on Noncommutative Curved Spacetimes |
| title_full |
Dirac Operators on Noncommutative Curved Spacetimes |
| title_fullStr |
Dirac Operators on Noncommutative Curved Spacetimes |
| title_full_unstemmed |
Dirac Operators on Noncommutative Curved Spacetimes |
| title_sort |
dirac operators on noncommutative curved spacetimes |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149372 |
| citation_txt |
Dirac Operators on Noncommutative Curved Spacetimes / A. Schenkel, C.F. Uhlemann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 36 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT schenkela diracoperatorsonnoncommutativecurvedspacetimes AT uhlemanncf diracoperatorsonnoncommutativecurvedspacetimes |
| first_indexed |
2023-05-20T17:32:51Z |
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2023-05-20T17:32:51Z |
| _version_ |
1796153542469222400 |