Group-quantization of nonlinear sigma models: Particle on S2 revisited

We present the quantum mechanics of “partial-trace” nonlinear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly developed. As a remarkable feature, no explicit constraint treatment is required nor ordering ambiguities do appear. Moreover, the energy spectrum is recovered without extra terms in the curvature of the sphere.