The classical limit of so(3) compact quantum systems

Abstract

In a paper by Fawcett and Bracken (1991), the classical limit of ordinary non-compact quantum systems is considered in terms of the contraction of the underlying kinematical Lie algebra (the Weyl-Heisenberg algebra) and its representations to the Abelian Lie algebra of the same dimension and its representations. Some of those ideas are adapted to discuss in similar terms, the classical limit of compact quantum systems whose underlying kinematical algebras are of the special orthogonal type. The classical dynamical system that results from the classical limit of compact quantum mechanical system will be called a 'compact classical system'. Poisson brackets for such 'compact classical systems' have already been given in the literature and the recovery of the Poisson bracket for so(3) compact classical systems is demonstrated in terms of the contraction limit.