International journal of modern physics. A, Particles and fields, gravitation, cosmology vol:9 issue:23 pages:4149-4168
The phase space of a particle on a group manifold can be split into left and right sectors, in close analogy with the chiral sectors in Wess-Zumino-Witten models. We perform a classical analysis of the sectors, and geometric quantization in the case of SU(2). The quadratic relation, classically identifying SU(2) as the sphere S3, is replaced quantum-mechanically by a similar condition on noncommutative operators (''quantum sphere''). The resulting quantum exchange algebra of the chiral group variables is quartic, not quadratic. The fusion of the sectors leads to a Hilbert space that is subtly different from the one obtained through a more direct (unsplit) quantization.