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.

18 pages

References in corpus (4)

• Static properties of chiral models with SU(3) group structure
• Stückelberg Field Shiftting Quantization of Free-Particle on D-Dimensional Sphere
• On the Hamilton-Jacobi equation for second class constrained systems
• Constraint structure of O(3) nonlinear sigma model revisited

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• New class of solutions in the non-minimal O(3)-sigma model
• Gauge invariant counterparts and quantization of systems under holonomic constraints
• Canonical quantization of nonlinear sigma models with theta term, with applications to symmetry-protected topological phases
• Differential configurational complexity and phase transitions of the BPS solutions in the O(3)-sigma model
• Underlying gauge symmetries of second-class constraints systems