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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 249
Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice Z_N-Higgs Models J. C. A. Barata, F. Nill
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.
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