高阶微商场论中奇异拉氏量系统的量子正则对称性

QUANTAL CANONICAL SYMMETRY FOR A SYSTEM WITH SINGULAR HIGHER-ORDER LAGRANGIAN IN FIELD THEORIES

给出了高阶徽商场论中奇异拉氏量系统规范生成元的构成.从相空间中Green函数的生成泛函出发,导出了约束Hamilton系统正则形式的Ward恒等式.指出该系统的量子正则方程与由Dirac猜想得到的经典正则方程不同.给出了与Chern-Simons理论等价的一个广义动力学系统的量子化.将正则Ward恒等式初步应用于该系统,不作出对正则动量的路径积分,也可导出场的传播子与正规顶角之间的某些关系.

An algorithm to construct the generator of gauge transformation for a system with singular higher-order Lagranian in field theories is given. Starting from generating functional of Green function in phase space, the Ward identities in canonical formalism for the constrained Hamiltonian system are deduced. It is pointed out that the quantal canonical equation for such a system deffers from the classical canonical equation, arising from the fact that Dirac conjecture is valid. The quantization for a generalized dynamical system which can be equivalent to Chern-Simons theory is given. With preliminary application of canonical Ward identities to such a system, some relationships among the vertices and propagators for the fields can be deduced without carrying out the integration for canonical momenta in phase space path integral.