奇异拉氏量系统相空间路径积分中的整体对称性

Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian

基于奇异拉氏量系统 Green 函数的相空间生成泛函,导出了相空间中整体变换下的 Ward 恒等式和整体对称下的量子守恒律.一般它有别于经典Noether 守恒律.用于杨-Mills 理论,导出了 BRS 变换下的 Ward-Takahashi恒等式和 BRS 守恒量;用于非 Abel-Chern-Simons 理论,导出了系统的量子角动量,它有别于经典角动量在于计及了鬼粒子对角动量的贡献.

Based on the phase-space generating functional of a system with a singular Lagrangian,the Ward identities under global transformation in phase space are de- duced.The quantum conservation laws under the global symmetry transiormation are also derived which is in general different from classical Hoether's ones.The preliminary application of our formulation to the Yang-Mills theory the Ward- Takahashi identity and BRS conserved quantity for BRS transformation are presented. Applying to non-Abelian-Chern-Simons theory the quantum conserved angular mo- mentum (QCAM) are obtained.The QCAM differs from classical one because the for- mer needs to take into account the distribution of angular momentum of ghost in non-Abelian-Chern-Simons theory.