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Zap. Nauchn. Sem. POMI, 2006, Volume 331, Pages 199–220 (Mi znsl255)  

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.

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English version:
Journal of Mathematical Sciences (New York), 2007, 141:4, 1494–1505

Bibliographic databases:

UDC: 517.958, 530.145
Received: 27.06.2006
Language: English

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

Citation in format AMSBIB
\Bibitem{Ste06}
\by D.~Sternheimer
\paper Some reflections on mathematicians' views of quantization
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XIV
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 331
\pages 199--220
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl255}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2251347}
\zmath{https://zbmath.org/?q=an:1096.53058}
\elib{http://elibrary.ru/item.asp?id=9172491}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 141
\issue 4
\pages 1494--1505
\crossref{https://doi.org/10.1007/s10958-007-0054-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846829892}


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  • Записки научных семинаров ПОМИ
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