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arXiv · 1311.1360

Geometric quantization of Dirac manifolds

Yuji Hirota
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Abstract

We define prequantization for Dirac manifolds to generalize known procedures for Poisson and (pre) symplectic manifolds by using characteristic distributions obtained from 2-cocycles associated to Dirac structures. Given a Dirac manifold $(M,D)$, we construct Poisson structure on the space of admissible functions on $(M,D)$ and a representation of the Poisson algebra to establish the prequantization condition of $(M,D)$ in terms of a Lie algebroid cohomology. Additional to this, we introduce a polarization for a Dirac manifold $M$ and discuss procedures for quantization in two cases where $M$ is compact and where $M$ is not compact.

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Yuji Hirota. 2013-11-06. Geometric quantization of Dirac manifolds. https://arxiv.org/abs/1311.1360

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