Dyonic Sectors and Intertwiner Connections in 2+1Dimensional Lattice Higgs Models
Abstract
We construct dyonic states in 2+1dimensional 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1998
 DOI:
 10.1007/s002200050273
 arXiv:
 arXiv:hepth/9612007
 Bibcode:
 1998CMaPh.191..409B
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Lattice;
 Mathematical Physics
 EPrint:
 61 pages. LaTeX. AmsTeX fonts used.