GROUP-THEORETICAL FORMALISM OF QUANTUM MECHANICS AND CLASSICAL-QUANTUM CORRESPONDENCE

GROUP-THEORETICAL FORMALISM OF QUANTUM MECHANICS AND CLASSICAL-QUANTUM

CORRESPONDENCE

作者：顾雁;;

作者机构：Department of Physics, Lanzhou University, Lanzhou 730000;and Institute of Theoretical Physics, Academia Sinica, Beijing 100080, PRC;

来源：中国科学

年：1992

卷：000

期：002

页码：P.200-210

页数：11

中图分类：N

正文语种：CHI

关键词：geometric quantization Lie-Poisson manifold group-theoretical formalism of quantum mechanics.

摘要：This article presents a mathematical framework for group-theoretical formalism of quan-tum mechanics and discusses the geometric quantization of the classical systems associatedwith a Lie group. The classical-quantum correspondence is realized by identifying quantumobservable algebra and its classical analogue with the set of distributions with compact sup-ports OD a Lie group and on the associated Lie algebra respectively, both having a convolu-tion-type associative algebraic structure. The general mathematical constructs are