高阶微商系统Dirac猜想的一个反例  

A counterexample of Dirac's conjecture for a system with a higher-order singular Lagrangian

作　　者：李爱民[1] 张晓沛[1] 李子平[1] 

机构地区：[1]北京工业大学数理学院,北京100022

出　　处：《物理学报》2003年第5期1057-1060,共4页Acta Physica Sinica

基　　金：北京市自然科学基金 (批准号 :1942 0 0 5 )资助的课题~~

摘　　要：由扩展正则作用量导出了高阶微商奇异Lagrange量系统的扩展正则Noether恒等式 .从广义约束Hamilton系统相空间中对称性分析 ,给出高阶微商系统Dirac猜想的一个反例 .用正则Noether定理、正则Noether恒等式和扩展正则Noether恒等式说明在此反例中Dirac猜想失效 。The extended canonical Noether identities derived from an extended action in the phase space for a system with a higher-order singular Lagrangian are formulated. Based on the canonical symmetries of generalized constrained Hamiltonian systems, a counterexample to a conjecture of Dirac is given. Using the canonical first Noether theorem and canonical Noether identities and the extended canonical Noether identities, we have shown that Dirac's conjecture fails for a system with a higher-order singular Lagrangian in which there is no linearization of constraint in our treatment.

关 键 词：高阶微商系统 DIRAC猜想 扩展正则作用量 广义约束Hamilton系统 对称性 相空间 奇异Lagrange量 扩展正则Noether恒等式 量子场论 规范场 

分 类 号：O413.4[理学—理论物理]