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

TL;DR

This paper systematically analyzes the Wess-Zumino-Witten model using symplectic methods, revealing its connections to Chern-Simons theory, quantum representations, and braid group structures.

Contribution

It introduces a symplectic framework for the WZW model, linking it to Chern-Simons theory and deriving key quantum and topological structures.

Findings

Relationship between WZW and Chern-Simons models established

Derived the Knizhnik-Zamolodchikov equation

Discussed holonomy and R-matrix representations of braid groups

Abstract

A systematic description of the Wess-Zumino-Witten model is presented. The symplectic 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 projective representation 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 $\check R$-matrix representation of braid group are discussed.