Dirac-type operators on curved spaces and the role of Killing-Yano tensors

摘要

We consider the Dirac equation in curved backgrounds and investigate the role of Killing-Yano tensors in constructing Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT space. We investigate the gravitational anomalies for generalized Euclidean Taub-NUT metrics that admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem.