GEOMETRIC APPROACH TO QUANTUM ANOMALIES.

研究了反常规范理论作为约束系统的情况。手征反常对正则结构的影响首先在非线性σ模型中考察，然后在费米子理论中考察。本文系统地研究了Gauss定律约束的破缺以及其中的反常交换子，引入规范场的内禀质量项，使Gauss定律关系作为第二类约束求解成为可能，并使A-la-Dirac系统成为可能。基于规范对称的Ward-Takahashi恒等式，我们在路径积分方法的框架下研究了反常费米子理论，第二部分利用Batalin，Fradkin和Vilkovisky发展的广义Hamilton形式，对四维拓扑Yang-Mills理论和二维拓扑σ模型进行了BRST量子化。

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear sigma-model and later for fermionic theory. The breakdown of Gauss law constraints and the anomalous commutators among them are studied in a systematic way.An intrinsic mass term for gauge fields makes it possible to solve the Gauss law relations as second class constraints and to quantize the system A la Dirac. Based upon the Ward-Takahashi identities for gauge symmetry, we investigate anomalous fermionic theory within the framework of path integral approach.As a second topic, we have BRST-quantized the topological Yang-Mills theory in four dimensions and the topological sigma-model in two dimensions, using the generalized Hamiltonian formalism developed by Batalin, Fradkin and Vilkovisky.