约束Hamilton系统量子理论中的Noether定理和Poincaré-Cartan积分不变量

Noether Theorem and Poincare - Cartan Integral Invariant in Quantum Case for a Constrained Hamilton System

基于有限自由度约束Hamilton系统的Green函数的相空间生成泛函,导出了该系统在相空间中整体对称下的量子形式Noether定理.根据生成泛函在相空间中的平移不变性,得到了该系统的量子水平Poincaré-Cartan积分不变量,并讨论了与经典结果的对比.

Based on the phase-space generating functional of Green function for a constrained Hamiltonian system with finite degree of freedom, the Noether theorem in quantum case under the global symmetry in phase space is derived for such a system. According to the translation-invariance of generating functional in phase space, the Poincare-Cartan integral invariant at the quantum level is deduced. The comparison of it with the classical results is discussed.