WZW模型和规范场论的辛方法

Symplectic Approach of Wess-Zumino-Witten Model and Gauge Field Theories

本文系统讨论Ｗｅｓｓ－Ｚｕｍｉｎｏ－Ｗｉｔｔｅｎ模型，给出了ＷＺＷ模型的辛理论，得到ＷＺＷ模型与Ｃｈｅｒｎ－Ｓｉｍｏｎｓ模型的关系．并且还给出了ＷＺＷ模型几何量子化理论以及圈群的投影表示．本文还研究了三种不同情况下规范场的动量矩映射，通过Ｍａｒｓｄｅｎ－Ｗｅｉｎｓｔｅｉｎ约化，得到Ｇａｕｓｓ约束；还得到ｋｏｈｎｏ联络，证明了这个联络是平坦的，它的ｈｏｌｏｎｏｍｙ表示则给出了辫群的表示．本文内容散见於近代物理文献，从物理观点看不是新的，但是本文对ＷＺＷ模型的讨论和简述在数学上是严格的。

A systematic description of the Wess-Zumino-Witten model is presented. The sym-plectic method plays the major role in this paper and also gives the relationship between the WZW model and the Chern-Simons model,The quantum theory is obtained to give the prpjective represen-tation of the Loop group.The Gauss constraints for the connection whose curvature is only focused on several fixed points are solved.The Kohno connection and the Knizhnik-Zamolodchikov equation are derived.The holonomy representation and R-matrix representation of braid group are discussed.