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A Groenewold-Van Hove Theorem for S^2

Mark J. Gotay·Hendrik Grundling·C. A. Hurst
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Abstract

We prove that there does not exist a nontrivial quantization of the Poisson algebra of the symplectic manifold S^2 which is irreducible on the subalgebra generated by the components {S_1,S_2,S_3} of the spin vector. We also show that there does not exist such a quantization of the Poisson subalgebra P consisting of polynomials in {S_1,S_2,S_3}. Furthermore, we show that the maximal Poisson subalgebra of P containing {1,S_1,S_2,S_3} that can be so quantized is just that generated by {1,S_1,S_2,S_3}.

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BibTeXRIS

Mark J. Gotay, Hendrik Grundling, C. A. Hurst. 1995-02-23. A Groenewold-Van Hove Theorem for S^2. https://arxiv.org/abs/dg-ga/9502008

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