Field theory of anyons in the lowest Landau level

TL;DR

This paper develops a field theory for anyons confined to the lowest Landau level, connecting particle descriptions to field theories with modified commutation relations, and relates it to edge excitations in quantum Hall systems.

Contribution

It introduces a novel field theoretical framework for anyons in the lowest Landau level derived from N-particle descriptions, linking to gauge potentials and edge states.

Findings

Fields on the circle with modified commutation relations

Connection between particle and field descriptions of anyons

Relation to edge excitations in quantum Hall systems

Abstract

We construct a field theory for anyons in the lowest Landau level starting from the $N$-particle description, and discuss the connection to the full field theory of anyons defined using a statistical gauge potential. The theory is transformed to free form, with the fields defined on the circle and satisfying modified commutation relations. The Fock space of the anyons is discussed, and the theory is related to that of edge excitations of an anyon droplet in a harmonic oscillator well.