相空间Noether恒等式和Dirac猜想  

Noether Identities in Phase-space and Dirac's Conjecture

作　　者：王永龙[1] 李子平[1] 

机构地区：[1]北京工业大学应用数理学院,北京100022

出　　处：《北京工业大学学报》2005年第1期97-101,共5页Journal of Beijing University of Technology

基　　金：北京工业大学校青年基金资助课题(JQ0607200370).

摘　　要：基于含第一类和第二类约束Hamilton系统的运动方程,重新分析了Dirac猜想的提出.在约束乘子是 时间和正则变量的函数,以及规范生成元的组合系数为时间、正则变量和约束乘子的函数一般情况下,建立了扩 展正则Noether恒等式(ECNI).最后从相空间正则Noether恒等式(CNI)和ECNI出发讨论了一个Dirac猜想反 例,说明在此情形下Dirac猜想仍然失效.Based on the equations of motion for a Hamiltonian system with primary first-class and second-class constraints, the authors discuss the origin of Dirac's conjecture at first. Then it is supposed that the constraint multipliers are the functions of time and canonical variables, and combination coefficients in the gauge generator are the functions of time, canonical variables and constraint multipliers, the extended canonical Noether identities (ECNI) are deduced. Finally, a counter-example of Dirac's conjecture is discussed based on the phase-space canonical Noether identities (CNI) and ECNI, and the result shows that the Dirac's conjecture is still invalid in this circumstance.

关 键 词：约束HAMILTON系统 DIRAC猜想 规范生成元 Noether恒等式 

分 类 号：O412.3[理学—理论物理] O413.3[理学—物理]