量子正则Noether定理

Canonical Noether Theorem at the Quantum Level

从有限自由度系统相空间Green函数的生成泛函出发 ,导出了量子情形下的正则Noether定理 ,其中不存在基态符号 .用于Emden方程 ,说明了经典守恒量在量子水平下不再保持 .用于电子 -声子相互作用系统 ,表明在这个系统中 ,经典正则对称性和它所对应的守恒量在量子理论中仍然是保持的 。

Based on the phase-space generating functional of Green function for a regular/singular system with finite degrees of freedom, the canonical Noether theorem at the quantum level is derived. Appling to the Emden's equation ,the conserved quantity at the classical level may not hold true at the quantum level. Appling to the electron-phonon system, the conserved quantity at the classical level still hold true at the quantum level , the total conserved angular momentum at the quantum level for this system should include the spin angular momentum of electron.