An obstruction to quantization of the sphere

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In the standard example of strict deformation quantization of the symplectic sphere S2, the set of allowed values of the quantization parameter h is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including S2) in which h 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.
Original languageEnglish
Pages (from-to)675-699
Number of pages25
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - Nov 2008


  • Mathematical Physics

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