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


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.


Poisson Bracket Symplectic Manifold Poisson Structure Jacobi Identity Deformation Quantization 
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I would like to thank Klaas Landsman and Marc Rieffel for their comments, and Ryszard Nest for encouraging me to investigate this question.

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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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