Quantum symmetries in discrete gauge theories

摘要: Abstract 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 subgroup H. identify quantumnumbers electrically magnetically charged sectors remaining theory, show that on quantum level symmetry H extended (quasi-triangular) Hopf algebra D(H). A conjugacy class paired with centralizer representation forms an irreducible representation. The fusion rules for arbitrary anyons are completely determined by nontrivial comultiplication (i.e. tensorproduct) this algebra. It allows clear interpretation Cheshire charge. Also braid-matrix R , which determines statistical two particle Aharonov-Bohm scattering, fixed satisfies Yang-Baxter equation. Most our considerations relevant (3+1)-dimensional space time as well.