QUANTUM GROUPS IN THE HIGGS PHASE

In the Higgs phase we may be left with a residual finite symmetry grou p H of the condensate. The topological interactions between the magnet ic and electric excitations in these so-called discrete H gauge theori es are completely described by the Hopf algebra or quantum group D(H). In 2 + 1 dimensional space time we may add a Chern-Simons term to suc h a model. This deforms the underlying Hopf algebra D(H) into the quas i-Hopf algebra D omega(II) by means of a and cocycle omega on H. Conse quently, the finite number of physically inequivalent discrete Ii gaug e theories obtained in this way are labelled by the elements of the co homology group H-3(H,U(I)). We briefly review the above results in the se notes. Special attention is given to the Coulomb screening mechanis m operational in the Higgs phase. This mechanism screens the Coulomb i nteractions, but not the Aharonov-Bohm interactions.