CHIRAL QUANTIZATION ON A GROUP MANIFOLD

The phase space of a particle on a group manifold can be split into le ft 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 relati on, classically identifying SU(2) as the sphere S3, is replaced quantu m-mechanically by a similar condition on noncommutative operators (''q uantum 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 obtaine d through a more direct (unsplit) quantization.