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The Gauged O(3) Sigma Model: Schrödinger Representation and Hamilton-Jacobi Formulation

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.