Symplectic Dirac Operators on Kähler Manifolds

Abstract

The notion of symplectic spinors over a symplectic manifold was already introduced by B. Kostant in 1974 as a tool in his theory of geometric quantization. We observed that it is possible to define canonical symplectic Dirac operators acting on symplectic spinor fields in a similar way as one knows it from the Dirac operator on Riemannian manifolds. In this paper we study symplectic Dirac operators provided that the underlying manifold is a Kähler manifold with the Kähler form as symplectic structure.