Regensburg 1998 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 2: Hauptvorträge II

MP 2.1: Invited Talk

Monday, March 23, 1998, 14:00–14:45, H46

Dyonic Sectors and Intertwiner Connections in 2+1-dimensional Lattice Z_N-Higgs Models — •Florian Nill² and Joao Carlos Alves Barata¹ — ¹Instituto de Física da Universidade de São Paulo, P.O. Box 66318, São Paulo 05315 970, SP, Brasil. — ²Inst. theor. Physik, FU-Berlin, Arnimallee 14, D-14195 Berlin

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.

[1] J. C. A. Barata, F. Nill, hep-th/9612007, to appear in Comm. Math. Phys.