量子水平的Noether恒等式

Noether Identities at the Quantum Level

基于Green函数的相空间生成泛函 ,导出了定域变换下的量子正则Noether恒等式 ;对规范不变系统 ,导出了位形空间中的量子Noether恒等式 .指出在某些情形下由量子Noether恒等式可导致系统的量子守恒律 ,这种求量子守恒律的方法与量子Noether(第一 )定理的程式不同 .用于非AbelChern Simons(CS)理论 ,求出了BRS和PBRS守恒荷 ,这两个守恒荷完全不同 .

Based on the phase-space generating functional of Green function, the canonical Noether identities under the local transformation at the quantum level have been derived. For the gauge-invariant system, the quantal Noether identities in configuration space have been also deduced. It is pointed out that in certain cases the quantal Noether identities may be converted to quantal conservation laws of the system. This method for obtaining the quantal conservation laws is significantly different from the first Noether theorem at the quantum level. The application to non-Abelian CS theories is studied, the quantal conserved BRS and PBRS charges are obtained, and these two conserved charges are totally different.