广义Noether定理和Poincaré-Cartan积分不变量  

Generalized Canonical Noether Theorem and Poincare-Cartan Integral Invariant

作　　者：李瑞洁[1] 李子平[2] 

机构地区：[1]华北电力大学(北京)基础部北京 102206 [2]北京工业大学应用数理学院

出　　处：《北京工业大学学报》2002年第3期329-333,共5页Journal of Beijing University of Technology

摘　　要：指出约束在包含时间在内的正则变量的总变分下不变时,仍可导出高阶微商奇异Iagrange量系统经典正则Noether定理和Poincare-Cartan（PC）积分不变量;不同的是,在以往文献中要求约束在正则变量的等时变换下不变.基于相空间Green函数的生成泛函,导出了高阶微商奇异Lagrange量系统在量子水平下的广义Noether定理和PC积分不变量;证明了当变换的Jacobi行列式不为1时,仍可导出量子PC积分不变量;将量子情况下的结果与经典结果作了对比.The constraints are invariant under the total variation of canonical variables including time, we can also deduce the classical canonical Noether theorem and Poincare-Cartan integral invariant for a system with a singular higher-order Lagrangian, which differs from the previous work to require that the constraints are invariant under the simultaneous variations of canonical variables. Based on the phase space generating function of Green function, the generalized first Noether theorem and Poincare-Cartan integral invariant in the quantum case for a system with a singular higher-order Lagrangian are derived. For the case in which the Jacobian of the transformation does not equal to unity, the quantal Poincare-Cartan integral invariant can be still derived. The comparisons of the results at the quantum level with those in classical theories are discussed.

关 键 词：广义Noether定理 高阶微商奇异Lagrange量系统 Poincaré-Cartan积分不变量 对称性 正则变量 约束 动力学 

分 类 号：O316[理学—一般力学与力学基础]