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.
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Acknowledgments
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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hawkins, E. An Obstruction to Quantization of the Sphere. Commun. Math. Phys. 283, 675–699 (2008). https://doi.org/10.1007/s00220-008-0517-2
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DOI: https://doi.org/10.1007/s00220-008-0517-2