GEOMETRIC APPROACH TO QUANTUM ANOMALIES.

研究了作为约束系统的反常规范理论。首先研究了非线性σ模型和费米子理论中手性异常对正则结构的影响。系统地研究了高斯定律约束的击穿和其中的反常换向子。规范场的内在质量项使得求解高斯定律关系作为第二类约束和量子化系统成为可能。基于规范对称的Ward-Takahashi恒等式，研究了路径积分方法框架下的异常费米子理论。作为第二个主题，我们使用Batalin， Fradkin和Vilkovisky发展的广义哈密顿形式主义，在四维空间对拓扑Yang-Mills理论和二维空间的拓扑sigma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.