Representation Theory of Chern Simons Observables

Details Representation Theory of Chern Simons Observables Representation Theory of Chern Simons Observables

1995-03-29

arxiv.org/abs/q-alg/9503016v1

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, latex

Scientific paper

Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the moduli space of flat connections on a 2-dimensional surface. In this paper we classify unitary representations of this new algebra and identify the corresponding representation spaces with the spaces of conformal blocks of the WZW model. The mapping class group of the surface is proved to act on the moduli algebra by inner automorphisms. The generators of these automorphisms are unitary elements of the moduli algebra. They are constructed explicitly and proved to satisfy the relations of the (unique) central extension of the mapping class group.

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