Abstract
Motivated by a recent paper of Fock and Rosly [6] 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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Communicated by G. Felder
Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821-304 and by the Federal Ministry of Science and Research, Austria
Part of project P8916-PHY of the ‘Fonds zur Förderung der wissenschaftlichen Forschung in Österreich’
Supported in part by DOE Grant No DE-FG02-88ER25065;
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Alekseev, A.Y., Grosse, H. & Schomerus, V. Combinatorial quantization of the Hamiltonian Chern-Simons theory I. Commun.Math. Phys. 172, 317–358 (1995). https://doi.org/10.1007/BF02099431
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DOI: https://doi.org/10.1007/BF02099431