The Dirac operator on symplectic spinors |
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Authors: | Katharina Habermann |
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Affiliation: | (1) Mathematisches Institut, Ruhr — Universität Bochum, 44780 Bochum, Germany |
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Abstract: | Symplectic spinors were introduced by B. Kostant in [4] in the context of geometric quantization. This paper presents further considerations concerning symplectic spinors. We define the spinor derivative induced by a symplectic covariant derivative. We compute an explicit formula for this spinor derivative and prove some elementary properties. This makes it possible to define the symplectic Dirac operator in a canonical way. In case of a symplectic and torsion-free covariant derivative it turns out to be formally selfadjoint. |
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Keywords: | Symplectic spinors symplectic Dirac operator |
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