Department of Theoretical Physics,

National Institute of Physics and Nuclear Engineering,

Magurele, P.O.Box MG-6, 76900 Bucharest, ROMANIA

E-mail: mvisin@theory.nipne.ro, mvisin@ifin.nipne.ro

**Symmetries and supersymmetries of the Dirac-type operators
on curved spaces**

**Abstract:**

The continuous and discrete symmetries of the Dirac-type operators
constructed with Killing-Yano tensors are studied in manifolds of arbitrary
dimensions. The covariantly constant Killing-Yano tensors realize certain
square roots of the metric tensor. Such a Killing-Yano tensor produces
simultaneously a Dirac-type operator and the generator of a one-parameter
Lie group connecting this operator with the standard Dirac one. The briefly
presented examples are the Euclidean Taub-NUT space and Minkowski spacetime.

**References:**

- M. Visinescu, Int. Journ. Mod. Phys. A17, 1049 (2002)
- I.I.Cotaescu and M.Visinescu, J. Math. Phys. 43,2978 (2002); hep-th/0107205
- I.I.Cotaescu and M.Visinescu, Gen. Rel. Grav.35, 389 (2003); hep-th/0202034
- I.I.Cotaescu and M.Visinescu, hep-th/0301108