An Obstruction to Quantization of the Sphere

Details An Obstruction to Quantization of the Sphere An Obstruction to Quantization of the Sphere

2007-06-20

arxiv.org/abs/0706.2946v2

Physics

Mathematical Physics

23 page. v2: changed sign convention

Scientific paper

10.1007/s00220-008-0517-2

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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