Chiral Quantization on a Group Manifold

The phase space of a particle on a group manifold can be split in 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 the 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 non-commutative 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 by a more direct (un–split) quantization. Onderzoeker IIKW, Belgium. Supported in part by KBN Grant 2 00 95 91 01. On leave from IFT, University of Wroc law, Poland Bevoegdverklaard Navorser NFWO, Belgium