Fermion on curved spaces, symmetries, and quantum anomalies
We review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved background...
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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146084 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fermion on curved spaces, symmetries, and quantum anomalies / M. Visinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146084 |
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irk-123456789-1460842019-02-08T01:23:12Z Fermion on curved spaces, symmetries, and quantum anomalies Visinescu, M. We review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. The gravitational and axial anomalies are studied for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. Using the Atiyah-Patodi-Singer index theorem for manifolds with boundaries, it is shown that the these metrics make no contribution to the axial anomaly. 2006 Article Fermion on curved spaces, symmetries, and quantum anomalies / M. Visinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 83C47; 83C40; 83C20 http://dspace.nbuv.gov.ua/handle/123456789/146084 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 review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. The gravitational and axial anomalies are studied for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. Using the Atiyah-Patodi-Singer index theorem for manifolds with boundaries, it is shown that the these metrics make no contribution to the axial anomaly. |
| format |
Article |
| author |
Visinescu, M. |
| spellingShingle |
Visinescu, M. Fermion on curved spaces, symmetries, and quantum anomalies Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Visinescu, M. |
| author_sort |
Visinescu, M. |
| title |
Fermion on curved spaces, symmetries, and quantum anomalies |
| title_short |
Fermion on curved spaces, symmetries, and quantum anomalies |
| title_full |
Fermion on curved spaces, symmetries, and quantum anomalies |
| title_fullStr |
Fermion on curved spaces, symmetries, and quantum anomalies |
| title_full_unstemmed |
Fermion on curved spaces, symmetries, and quantum anomalies |
| title_sort |
fermion on curved spaces, symmetries, and quantum anomalies |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146084 |
| citation_txt |
Fermion on curved spaces, symmetries, and quantum anomalies / M. Visinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT visinescum fermiononcurvedspacessymmetriesandquantumanomalies |
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2023-05-20T17:23:46Z |
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2023-05-20T17:23:46Z |
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1796153199171731456 |