Electrically and Magnetically Charged States and Particles in the 2+1-Dimensional Z_N-Higgs Gauge Model

TL;DR

This paper constructs and establishes the existence of electrically and magnetically charged states in a 2+1-dimensional Z_N-Higgs lattice gauge model, laying groundwork for studying anyonic statistics of these particles.

Contribution

It introduces methods to construct charged states in the model and proves their existence, advancing understanding of topological excitations in lattice gauge theories.

Findings

Existence of electrically charged states established.

Existence of magnetically charged states established.

Framework for future study of anyonic statistics developed.

Abstract

Electrically as well as magnetically charged states are constructed in the 2+1-dimensional Euclidean Z_N-Higgs lattice gauge model, the former following ideas of Fredenhagen and Marcu and the latter using duality transformations on the algebra of observables. The existence of electrically and of magnetically charged particles is also established. With this work we prepare the ground for the constructive study of anyonic statistics of multiparticle scattering states of electrically and magnetically charged particles in this model (work in progress).