Generalized Fuzzy Torus and its Modular Properties
We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy...
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| Дата: | 2013 |
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| 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/123456789/149352 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Generalized Fuzzy Torus and its Modular Properties / P. Schreivogl, H. Steinacker // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1493522019-02-22T01:22:54Z Generalized Fuzzy Torus and its Modular Properties Schreivogl, P. Steinacker, H. We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed. 2013 Article Generalized Fuzzy Torus and its Modular Properties / P. Schreivogl, H. Steinacker // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R60; 81T75; 81T30 DOI: http://dx.doi.org/10.3842/SIGMA.2013.060 http://dspace.nbuv.gov.ua/handle/123456789/149352 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 consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter τ. The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed. |
| format |
Article |
| author |
Schreivogl, P. Steinacker, H. |
| spellingShingle |
Schreivogl, P. Steinacker, H. Generalized Fuzzy Torus and its Modular Properties Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schreivogl, P. Steinacker, H. |
| author_sort |
Schreivogl, P. |
| title |
Generalized Fuzzy Torus and its Modular Properties |
| title_short |
Generalized Fuzzy Torus and its Modular Properties |
| title_full |
Generalized Fuzzy Torus and its Modular Properties |
| title_fullStr |
Generalized Fuzzy Torus and its Modular Properties |
| title_full_unstemmed |
Generalized Fuzzy Torus and its Modular Properties |
| title_sort |
generalized fuzzy torus and its modular properties |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149352 |
| citation_txt |
Generalized Fuzzy Torus and its Modular Properties / P. Schreivogl, H. Steinacker // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 20 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT schreivoglp generalizedfuzzytorusanditsmodularproperties AT steinackerh generalizedfuzzytorusanditsmodularproperties |
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2023-05-20T17:32:47Z |
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2023-05-20T17:32:47Z |
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1796153535957565440 |