Abstract

This article is a review of two original papers [1], [2]. We begin with a description of Kirillov symplectic form and quantum mechanics on coadjoint orbits of a simple Lie group. This theory may be generalized for the case of a Poisson-Lie group. Both these theories are important for understanding of the Chern-Simons model which may be treated as a 3D gauge theory interacting with coadjoint orbits sitting on Wilson lines. Due to topological nature of the Chern-Simons theory one can get rid of the gauge fields in exchange of modification of coadjoint theories. We discover that this modification is exactly the same as we find in the Poisson-Lie case.