176 research outputs found
Geometric quantization of Dirac manifolds
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 , we construct Poisson structure on the space of
admissible functions on and a representation of the Poisson algebra to
establish the prequantization condition of in terms of a Lie algebroid
cohomology. Additional to this, we introduce a polarization for a Dirac
manifold and discuss procedures for quantization in two cases where is
compact and where is not compact.Comment: 33 pages. errors and typos correcte
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