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

TL;DR

This paper applies the Hamilton-Jacobi method to an abelian Chern-Simons system, deriving equations of motion and reduced phase space without gauge fixing or Lagrange multipliers.

Contribution

It introduces a Hamilton-Jacobi approach to analyze the constrained abelian Chern-Simons system, avoiding gauge fixing and Lagrange multipliers.

Findings

Derived equations of motion as total differentials in multiple variables

Obtained canonical phase space coordinates and reduced Hamiltonian

Eliminated the need for gauge fixing or Lagrange multipliers

Abstract

The abelian Chern-Simons system is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. It is shown that their simultaneous solutions with the constraints lead to obtain canonical phase space coordinates and the reduced phase space Hamiltonian with out introducing Lagrange multipliers and with out any additional gauge fixing condition.