Anyons on the sphere: analytic states and spectrum

TL;DR

This paper develops an operator method to find exact energy eigenstates of anyons on a sphere under a magnetic field, linking the problem to integrable Calogero systems and expanding understanding of quantum anyons in curved geometries.

Contribution

It introduces an operator approach for diagonalizing the Hamiltonian of anyons on a sphere and derives exact eigenstates, extending known results from the plane to curved geometry.

Findings

Derived exact energy eigenstates for anyons on the sphere

Established partial correspondence with known plane eigenstates

Discussed potential connections with Calogero-type integrable systems

Abstract

We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial correspondence with the known exact eigenstates on the plane. We also comment on possible connections of this system with integrable systems of the Calogero type.