Obstruction Results in Quantization Theory
dg-ga
2009-10-28 v1 高能物理 - 理论
微分几何
量子物理
摘要
We define the quantization structures for Poisson algebras necessary to generalise Groenewold and Van Hove's result that there is no consistent quantization for the Poisson algebra of Euclidean phase space. Recently a similar obstruction was obtained for the sphere, though surprising enough there is no obstruction to the quantization of the torus. In this paper we want to analyze the circumstances under which such obstructions appear. In this context we review the known results for the Poisson algebras of Euclidean space, the sphere and the torus.
关键词
引用
@article{arxiv.dg-ga/9605001,
title = {Obstruction Results in Quantization Theory},
author = {Mark J. Gotay and Hendrik B. Grundling and Gijs M. Tuynman},
journal= {arXiv preprint arXiv:dg-ga/9605001},
year = {2009}
}
备注
34 pages, Latex. To appear in J. Nonlinear Science