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Fermion on curved spaces, symmetries, and quantum anomalies
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Fermion on curved spaces, symmetries, and quantum anomalies
Інший ID:
2000 Mathematics Subject Classification: 83C47; 83C40; 83C20
Посилання:
Fermion on curved spaces, symmetries, and quantum anomalies / M. Visinescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ.
Підтримка:
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.
Дата:
2006
Переглядів:
569
Завантажень:
281
Анотація:
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.
