Non-Abelian Chern-Simons models with discrete gauge groups on a lattice -: art. no. 187

We construct the local Hamiltonian description of the Chern - Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric-field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, the dihedral groups D(n).