场论中泛函积分表述中的正则对称性

对场采用泛函积分量子化,从正则变量表述的Green函数的生成泛函出发,分别导出了用非奇异拉氏量和奇异拉氏量描述的系统在相空间中的广义Ward恒等式,指出一般情况下奇异系统量子正则方程与Dirac猜想给出的正则方程是不同的,讨论了声子、电子和光子系统的奇异拉氏量描述,导出了该系统Green函数的生成泛函,给出了正则形式的广义Ward恒等式的初步应用。

Canonical Symmetries in Functional Integral Expression for Field Theories

Using functional integral quantization for the fields and starting from the generating functional of Green' s function in canonical formalism, the generalized Ward identities in the phase space for the system with regular or singular Lagrangian are derived, and it is pointed out that the quantum canonical equations for a system with singular Lagrangian are different from canonical equations obtained by using Dirac' s conjecture. The systems containing phonon, electron and photon can be described in terms of singular Lagrangian. The generating functional of Green's function is deduced and preliminary applications of generalized Ward identities are also given for such a system.