Chiral Quantization on a Group Manifold

Details Chiral Quantization on a Group Manifold Chiral Quantization on a Group Manifold

1993-09-18

arxiv.org/abs/hep-th/9309099v1

Int.J.Mod.Phys. A9 (1994) 4149-4168

Physics

High Energy Physics

High Energy Physics - Theory

25p, LaTeX, KUL-TF-93/41

Scientific paper

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 $S^3$, 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.

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