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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 331, Pages 199–220
(Mi znsl255)
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This article is cited in 2 scientific papers (total in 2 papers)
Some reflections on mathematicians' views of quantization
D. Sternheimerab a Université de Bourgogne
b Keio University
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.
Received: 27.06.2006
Citation:
D. Sternheimer, “Some reflections on mathematicians' views of quantization”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Zap. Nauchn. Sem. POMI, 331, POMI, St. Petersburg, 2006, 199–220; J. Math. Sci. (N. Y.), 141:4 (2007), 1494–1505
Linking options:
https://www.mathnet.ru/eng/znsl255 https://www.mathnet.ru/eng/znsl/v331/p199
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Abstract page: | 261 | Full-text PDF : | 122 | References: | 53 |
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