Geometric quantization of Dirac manifolds

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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.