Monatshefte für Mathematik

, Volume 96, Issue 4, pp 293–310 | Cite as

Geometric quantization on presymplectic manifolds

  • Izu Vaisman


In this paper, we discuss the possibilities of adapting geometric quantization to presymplectic manifolds, i.e., differentiable manifoldsM 2n+k (k>0) endowed with a closed 2-form ω of rank2n. We show that such an adaptation is possible in various manners, and that, as a general idea, it reduces the quantization onM to quantization on the symplectic quotientM/V, whereV is the foliation defined by the annihilator of ω.


Manifold General Idea Geometric Quantization Presymplectic Manifold 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Izu Vaisman
    • 1
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael

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