Fermion on Curved Spaces, Symmetries, and Quantum Anomalies

Details Fermion on Curved Spaces, Symmetries, and Quantum Anomalies Fermion on Curved Spaces, Symmetries, and Quantum Anomalies

2006-09-28

arxiv.org/abs/hep-th/0609207v2

SIGMA 2:083,2006

Physics

High Energy Physics

High Energy Physics - Theory

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (

Scientific paper

10.1063/1.2733191

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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