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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146084 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Fermion on curved spaces, symmetries, and quantum anomalies / M. Visinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Visinescu, M. 2019-02-07T09:07:28Z 2019-02-07T09:07:28Z 2006 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 https://nasplib.isofts.kiev.ua/handle/123456789/146084 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. This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). It is a pleasure to thank the organizers of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory for the invitation to present this work. This work is partially supported by a CEEX-MEC (Romania) Program. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Fermion on curved spaces, symmetries, and quantum anomalies Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Fermion on curved spaces, symmetries, and quantum anomalies |
| spellingShingle |
Fermion on curved spaces, symmetries, and quantum anomalies Visinescu, M. |
| 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 |
| author |
Visinescu, M. |
| author_facet |
Visinescu, M. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146084 |
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| 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. |
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AT visinescum fermiononcurvedspacessymmetriesandquantumanomalies |
| first_indexed |
2025-11-24T11:04:10Z |
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2025-11-24T11:04:10Z |
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1850845277757374464 |