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Communications in Mathematical Physics

, Volume 283, Issue 3, pp 675–699 | Cite as

An Obstruction to Quantization of the Sphere

  • Eli HawkinsEmail author
Open Access
Article

Abstract

In the standard example of strict deformation quantization of the symplectic sphere S2, the set of allowed values of the quantization parameter ħ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including S2) in which ħ can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing S2 is never connected.

Keywords

Poisson Bracket Symplectic Manifold Poisson Structure Jacobi Identity Deformation Quantization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I would like to thank Klaas Landsman and Marc Rieffel for their comments, and Ryszard Nest for encouraging me to investigate this question.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Institute for Mathematics, Astrophysics, and Particle PhysicsRadboud UniversityNijmegenThe Netherlands

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