Anyons, Deformed Oscillator Algebras and Projectors

TL;DR

This paper develops an algebraic framework using deformed oscillator algebras to analyze the many-anyon problem, introducing a Hamiltonian and angular momentum operator with a connected anyonic weight lattice.

Contribution

It introduces a novel algebraic approach based on deformed oscillator and projector algebras for studying many-anyon systems, extending the Calogero model formalism.

Findings

Existence of a unique ground state.

Complete connectivity of anyonic weight lattices.

Effective linearized analysis in the statistical parameter nu.

Abstract

We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter nu. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.