Barata J. C. A., Nill F.
Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice
Z_N-Higgs Models.
(577K, PostScript)
ABSTRACT. We construct dyonic states in 2+1-dimensional lattice Z_N-Higgs
models, i.e., states which are both, electrically and magnetically
charged. The associated Hilbert spaces carry charged representations
of the observable algebra, the global transfer matrix 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
depending on a path in the space of charge distributions. The
holonomy of this connection is given by Z_N-valued phases. This will
be the starting point for a construction of scattering states with
anyon statistics in a subsequent paper.