Journal of Mathematical Sciences

, Volume 141, Issue 4, pp 1494–1505 | Cite as

Some reflections on mathematicians’ views of quantization

  • D. Sternheimer


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.


Quantum Group Deformation Theory Symplectic Manifold Star Product Noncommutative Geometry 
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Copyright information

© Daniel Sternheimer 2007

Authors and Affiliations

  • D. Sternheimer
    • 1
    • 2
  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance
  2. 2.Department of MathematicsKeio UniversityYokohamaJapan

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