Combinatorial quantization of the Hamiltonian Chern-Simons theory I

Details Combinatorial quantization of the Hamiltonian Chern-Simons theory I Combinatorial quantization of the Hamiltonian Chern-Simons theory I

1994-03-10

arxiv.org/abs/hep-th/9403066v2

Commun.Math.Phys. 172 (1995) 317-358

Physics

High Energy Physics

High Energy Physics - Theory

49 pages. Some minor corrections, discussion of positivity improved, a number of remarks and a reference added)

Scientific paper

10.1007/BF02099431

Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *-operation and a positive inner product.

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