Poincare'-Cartan积分不变量的推广和Dirac猜想

数学物理学报 ›› 1997, Vol. 17 ›› Issue (2): 192-199.

Poincare'-Cartan积分不变量的推广和Dirac猜想

李子平¹, 唐太明²

1 北京工业大学六系北京 100022;
2 新疆师范大学数学系乌鲁木齐 830054

收稿日期:1995-06-19 出版日期:1997-04-26 发布日期:1997-04-26
基金资助:
国家自然科学基金和北京市自然科学基金

A Generalization of the Poincaré-Cartan Invarian and Dirac's Conjecture

Li Ziping¹, Tang Taiming²

Beijing University of Technology, Beijing 100022

Received:1995-06-19 Online:1997-04-26 Published:1997-04-26

摘要/Abstract

摘要： 该文将Poincaré-Cartan积分不变量推广到显含时间的高阶微商奇异拉氏量系统,研究了该不变量与正则方程、正则变换之间的联系,讨论了广义Poincaré-Cartan积分不变量与Dirac猜想的关系,以一个例子说明,对高阶微商奇异拉氏量系统,Dirac猜想是无效的.

关键词: 高阶微商拉氏量, 约束系统的Dirac理论, Poincaré-Cartan积分不变量

Abstract: We generalize Poincaré-Cartan integral invariant to a system with a singular higher-order Lagrangian which depends on time t explicitly, this invariant connected with the canonical equations and canonical transformation for the generalized constrained Hamiltonian system is studied. The connection between this invariant and Dirac's conjecture is discussed.An example shows that Dirac's conjecture fails for a system with a singular higher-order LagranJian.

Key words: higher-order derivative Lagrangian, Dirac's theory of constrained system, Poincaré-Cartan integral invariant

李子平, 唐太明. Poincare'-Cartan积分不变量的推广和Dirac猜想[J]. 数学物理学报, 1997, 17(2): 192-199.

Li Ziping, Tang Taiming. A Generalization of the Poincaré-Cartan Invarian and Dirac's Conjecture[J]. Acta mathematica scientia,Series A, 1997, 17(2): 192-199.