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Functorial geometric quantization and Van Hove's theorem

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Abstract

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 Schrödinger quantization and the prequantization/polarization theory of Kostant and Souriau.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Mark J. Gotay

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  1. Mark J. Gotay
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Gotay, M.J. Functorial geometric quantization and Van Hove's theorem. Int J Theor Phys 19, 139–161 (1980). https://doi.org/10.1007/BF00669766

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  • DOI: https://doi.org/10.1007/BF00669766

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