The Hamilton-Jacobi treatment for non-abelian Chern-Simons system

TL;DR

This paper applies the Hamilton-Jacobi method to analyze a non-abelian Chern-Simons system interacting with complex fields, deriving a reduced phase space Hamiltonian without gauge fixing and discussing quantization.

Contribution

It introduces a Hamilton-Jacobi approach to non-abelian Chern-Simons systems, avoiding gauge fixing and Lagrange multipliers, and explores quantization.

Findings

Reduced phase space Hamiltonian density obtained without gauge fixing.

Quantization of the non-abelian Chern-Simons system discussed.

Hamilton-Jacobi method effectively handles constraints in this system.

Abstract

The non-abelian Chern-Simons field interacting with $N$ component complex field is treated as a constrained system using the Hamilton-Jacobi approach. The reduced phase space Hamiltonian density is obtained without introducing Lagrange multipliers and with out any additional gauge fixing condition. The quantization of this system is also discussed.