An Obstruction to Quantization of the Sphere

Abstract

In the standard example of strict deformation quantization of the symplectic sphere $S^2$, the set of allowed values of the quantization parameter $\hslash$ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including $S^2$) in which $\hslash$ 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.

23 page. v2: changed sign convention

References in corpus (1)

• Strict quantizations of almost Poisson manifolds