Group-quantization of non-linear sigma models: particle on S^2 revisited

V. Aldaya, M. Calixto, J. Guerrero, F. F. López-Ruiz

Published 2008-07-16Version 1

We present the quantum mechanics of "partial-trace" non-linear 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.