Non-Abelian Chern-Simons Quantum Mechanics

TL;DR

This paper develops a classical and quantum model for non-Abelian Chern-Simons theory with point sources, unifying fractional spin, braid statistics, and the Knizhnik-Zamolodchikov equation through BRST quantization.

Contribution

It introduces a novel classical model for non-Abelian Chern-Simons theory coupled to sources and applies BRST quantization to unify key quantum phenomena.

Findings

Quantum mechanics derived from the model incorporates fractional spin.

The framework unifies braid statistics and the Knizhnik-Zamolodchikov equation.

Provides a consistent quantization approach for non-Abelian Chern-Simons systems.

Abstract

We propose a classical model for the non-Abelian Chern-Simons theory coupled to $N$ point-like sources and quantize the system using the BRST technique. The resulting quantum mechanics provides a unified framework for fractional spin, braid statistics and Knizhnik-Zamolodchikov equation.