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| _version_ | 1862536321875050496 |
|---|---|
| author | Visinescu, M. |
| author_facet | Visinescu, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-11-24T11:04:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146084 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T11:04:10Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Fermion on curved spaces, symmetries, and quantum anomalies Visinescu, M. |
| title | 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_short | Fermion on curved spaces, symmetries, and quantum anomalies |
| title_sort | fermion on curved spaces, symmetries, and quantum anomalies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146084 |
| work_keys_str_mv | AT visinescum fermiononcurvedspacessymmetriesandquantumanomalies |