Functorial geometric quantization and Van Hove's theorem

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A classical theorem of Van Hove in conjunction with a formalism developed by Weinstein is used to prove that a quantization functor does not exist. In the proof a category of exact transverse Lagrangian submanifolds is introduced which provides a functorial link between Schrodinger quantization and the prequantization/polarization theory of Kostant and Souriau.