Dirac-Type Operators on Curved Spaces and the Role of Killing–Yano Tensors

M. Visinescu

National Institute for Physics and Nuclear Engineering

Abstract: 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.

Keywords: Dirac operator, Killing–Yano tensors, Taub–NUT space, hidden symmetries.

DOI: 10.4213/tmf1846

 English version: Theoretical and Mathematical Physics, 2005, 144:1, 1054–1062

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