A Groenewold-Van Hove Theorem for S^2
dg-ga
2016-08-31 v1 High Energy Physics - Theory
Differential Geometry
Quantum Physics
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}.
Cite
@article{arxiv.dg-ga/9502008,
title = {A Groenewold-Van Hove Theorem for S^2},
author = {Mark J. Gotay and Hendrik Grundling and C. A. Hurst},
journal= {arXiv preprint arXiv:dg-ga/9502008},
year = {2016}
}
Comments
20 pages, AMSLaTeX