BRST Quantization And It's Application To Constrained Hamiltonian Systems

This thesis reviews the method of calculation of Hamiltonian system, three conditions that the system doesn't have constrains are discussed, and the examples of these cases are given. Thereafter, we summarize the intrinsic properties of BRST transformation, the canonical ward identities of phase space and the gauge generators, further sum up the first-class & the second-class constrains (in Hamiltonian system) and the relations between the first constraints and gauge transformation generators.The thesis deduces the generating functional of proper vertexes and BRST transformation of the system of matter field coupling to non-Abel gauge field, gives Noether conservation charge of BRST transformation, shows up the model's BRST transformation when the gauges are Lorentz, coulomb and radiation gauges, respectively, finishes the BRST quantization of ghost field in (1+2) dimensions model with non-Abel Chern-Simons term coupling to the scalar field, achieves the Lagrange density and Hamilton density under BRST transformation.According to the Dirac constrain theory and the extended condition, we deduce the gauge generators, show the BRST transformation of (1+1) dimension O(3) non-linear model under the new general condition. We first gain the new general commutation relations of ghost field, deduce the BRST charge from gauge generator, complete the general BRST quantization of the model, get Green function, connecting Green function and generating functional, gain three kinds of Ward identities. At last, We complete the BRST quantization of O(3) non-linear model with topological term in (1+1) dimensions space-time.