Quantum symmetries in discrete gauge theories

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We analyse the fusion, braiding and scattering properties of discrete non-abelian anyons. These occur in (2+1)-dimensional theories where a gauge group G is spontaneously broken down to some discrete subgroup H. We identify the quantumnumbers of the electrically and magnetically charged sectors of the remaining discrete gauge theory, and show that on the quantum level the symmetry group H is extended to the (quasi-triangular) Hopf algebra D(H). Most of our considerations are relevant for discrete gauge theories in (3+1)-dimensional space time as well.