The gauged O(3) sigma model: Schrödinger representation and Hamilton-Jacobi formulation

Abstract

We first study a free particle on an (n-1)-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schrödinger representation and a Hamilton-Jacobi formulation of the model. We thereby obtain the free particle energy spectrum corresponding to that of a rigid rotator. We extend these considerations to a modified version of the field theoretical O(3) nonlinear sigma model, and obtain the corresponding energy spectrum as well as BRST Lagrangian. © 2004 Published by Elsevier Inc.