Dyonic Sectors and Intertwiner Connections in 2+1-Dimensional Lattice -Higgs Models

We construct dyonic states in 2+1-dimensional lattice -Higgs models, i.e. states which are both, electrically and magnetically charged. These states are parametrized by , where ɛ and μ are -valued electric and magnetic charge distributions, respectively, living on the spatial lattice . The associated Hilbert spaces carry charged representations of the observable algebra , the global transfer matrix t and a unitary implementation of the group of spatial lattice translations. We prove that for coinciding total charges these representations are dynamically equivalent and we construct a local intertwiner connection , where is a path in the space of charge distributions . The holonomy of this connection is given by -valued phases. This will be the starting point for a construction of scattering states with anyon statistics in a subsequent paper. Received: 13 December 1996 / Accepted: 19 May 1997