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arXiv · 0706.2946

An Obstruction to Quantization of the Sphere

Eli Hawkins
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Abstract

In the standard example of strict deformation quantization of the symplectic sphere $S^2$, the set of allowed values of the quantization parameter $\hbar$ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including $S^2$) in which $\hbar$ 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 $S^2$ is never connected.

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Eli Hawkins. 2007-09-06. An Obstruction to Quantization of the Sphere. https://doi.org/10.1007/s00220-008-0517-2

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