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Some reflections on mathematicians’ views of quantization

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Abstract

We start with a short presentation of the difference in attitude between mathematicians and physicists even in their treatment of physical reality, and look at the paradigm of quantization as an illustration. In particular, we stress the differences in motivation and realization between the Berezin and deformation quantization approaches, exposing briefly Berezin’s view of quantization as a functor. We continue with a schematic overview of deformation quantization and of its developments in contrast with the latter and discuss related issues, in particular, the spectrality question. We end by a very short survey of two main avatars of deformation quantization, quantum groups and quantum spaces (especially noncommutative geometry) presented in that perspective. Bibliography: 74 titles.

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  1. Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon, France

    D. Sternheimer

  2. Department of Mathematics, Keio University, Yokohama, Japan

    D. Sternheimer

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This paper is dedicated to the memory of “Alik” Berezin

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 199–220.

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Sternheimer, D. Some reflections on mathematicians’ views of quantization. J Math Sci 141, 1494–1505 (2007). https://doi.org/10.1007/s10958-007-0054-0

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