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SIGMA 2 (2006), 083, 16 pages hep-th/0609207
https://doi.org/10.3842/SIGMA.2006.083
Contribution to the Proceedings of the O'Raifeartaigh Symposium
Fermion on Curved Spaces, Symmetries, and Quantum Anomalies
Mihai Visinescu
Department of Theoretical Physics, Institute for Physics
and Nuclear Engineering, Magurele, P.O.Box MG-6, Bucharest, Romania
Received September 28, 2006, in final form
November 21, 2006; Published online November 29, 2006
Abstract
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.
Key words:
spinning particles; Dirac type operators; gravitational anomalies; axial anomalies.
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