1993/11/28 by F. A. Bais, F.A. Bais, Mark de Wild Propitius +1
Physics and Astronomy · #Atomic and Subatomic Physics Research #Black Holes and Theoretical Physics #Topological Materials and Phenomena #hep-th
paper · pdf · doi:10.1007/bf01102213
published as Theor.Math.Phys. 98 (1994) 357-367; Teor.Mat.Fiz. 98 (1994) 509-523 · 19 pages in Latex, ITFA-93-30
arxiv created 1993/11/28 · openalex publication_date 1994/03/01 · arxiv updated 2009/11/30 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/29
In the Higgs phase we may be left with a residual finite symmetry group H of the condensate. The topological interactions between the magnetic- and electric excitations in these so-called discrete H gauge theories are completely described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle H. Consequently, the finite number of physically inequivalent discrete H gauge theories obtained in this way are labelled by the elements of the cohomology group H3(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at `The III International Conference on Mathematical Physics, String Theory and Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor. Math. Phys.)