Anyons, group theory and planar physics

TL;DR

This paper presents a unified formalism for describing relativistic and nonrelativistic anyons using coadjoint orbits of extended symmetry groups, including interactions with electromagnetic fields.

Contribution

It introduces the extended Poincaré and Galilei Maxwell groups to incorporate interactions into the coadjoint orbit framework for anyons.

Findings

Unified description of anyons in relativistic and nonrelativistic regimes

Inclusion of electromagnetic interactions via extended symmetry groups

Framework applicable to free and interacting cases

Abstract

Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell groups.