Multi Hamilton-Jacobi quantization of O(3) nonlinear sigma model

TL;DR

This paper applies the multi Hamilton-Jacobi formalism to the O(3) nonlinear sigma model, demonstrating its integrability and deriving the action through an extended phase space approach, aligning with Dirac's method.

Contribution

It introduces a multi Hamilton-Jacobi approach to the O(3) sigma model, providing a new perspective and confirming results with Dirac's method.

Findings

Confirmed integrability conditions match Dirac's method

Derived the system's action using extended phase space

Established equivalence with Dirac's quantization results

Abstract

The O(3) non-linear sigma model is investigated using multi Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method. By choosing an adequate extension of phase space we describe the transformed system by a set of three Hamilton-Jacobi equations and calculate the corresponding action.