Abstract.
Symplectic Dirac operators, acting on symplectic spinor fields introduced by B.~Kostant in geometric quantization, are canonically defined in a similar way as the Dirac operator on Riemannian manifolds. These operators depend on a choice of a metaplectic structure as well as on a choice of a symplectic covariant derivative on the tangent bundle of the underlying manifold. This paper performs a complete study of these relations and shows further basic properties of the symplectic Dirac operators. Various examples are given for illustration.
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Received: 1 July 1996 / Accepted: 24 September 1996
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Habermann, K. Basic Properties of Symplectic Dirac Operators . Comm Math Phys 184, 629–652 (1997). https://doi.org/10.1007/s002200050077
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DOI: https://doi.org/10.1007/s002200050077