Chiral Quantization on a Group Manifold

Zbigniew Hasiewicz; Przemysł{aw} Siemion; Walter Troost

doi:10.1142/s0217751x94001680

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arXiv · hep-th/9309099

Chiral Quantization on a Group Manifold

Zbigniew Hasiewicz·Przemysł{aw} Siemion·Walter Troost

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Abstract

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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Zbigniew Hasiewicz, Przemysł{aw} Siemion, Walter Troost. 1993-09-18. Chiral Quantization on a Group Manifold. https://doi.org/10.1142/s0217751x94001680

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