95-72 Mark J. Gotay, Hendrik Grundling, C.A. Hurst

A Groenewold-Van Hove Theorem for S^2 (58K, TeX) Feb 19, 95

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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 $\cal P$ 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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