约束Hamilton系统的对称性与守恒量的某些研究进展  

Symmetries and conserved quantities of constrained Hamiltonian systems

作　　者：郑明亮 冯鲜[1] ZHENG Mingliang;FENG Xian(School of Electrical and Mechanical Engineering,Taihu University of Wuxi,Wuxi 214064,China)

机构地区：[1]无锡太湖学院机电工程学院,江苏无锡214064

出　　处：《苏州科技大学学报（自然科学版）》2020年第3期8-14,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(21676031);江苏省高等学校自然科学基金资助项目(18KJB460027)。

摘　　要：介绍有关约束Hamilton系统的对称性与守恒量理论研究与应用发展。对约束Hamilton系统的结构特点和本质进行了总结和评价。在经典水平层面介绍了Noether对称性、Lie对称性、Mei对称性以及由它们导致的守恒量;在量子水平层面介绍了正则对称性,涉及Ward恒等式、量子守恒律和Poincare'-Cartan积分不变量。并提出了若干问题和进一步研究建议。We introduced the theoretical research and application of the symmetries and conserved quantities of the constrained Hamiltonian systems. The structural features and nature of the constrained Hamiltonian systems were summarized and reviewed. At the classical level,we introduced the Noether symmetry,Lie symmetry,Mei symmetry,and the conserved quantities caused by them. At the quantum level,we introduced the regular symmetry,including the Ward identity,the quantum conserved quantities and the Poincare’-Cartan integral invariants.Some questions and suggestions for further study were put forward.

关 键 词：约束HAMILTON系统 对称性 守恒量 量子 

分 类 号：O316[理学—一般力学与力学基础] O322[理学—力学]