Loop groups, anyons and the Calogero-Sutherland model

TL;DR

This paper develops a boson-anyon correspondence using loop group representations, computes correlation functions, and constructs eigenfunctions of the Calogero-Sutherland model through an anyonic algebra framework.

Contribution

It introduces a novel approach linking loop group representations to the Calogero-Sutherland model via an anyonic algebra, enabling explicit eigenfunction construction.

Findings

Computed all correlation functions of anyon fields.

Identified an operator with exchange relations as a second quantised CS Hamiltonian.

Constructed eigenfunctions of the CS model for all particle numbers and couplings.

Abstract

The positive energy representations of the loop group of U(1) are used to construct a boson-anyon correspondence. We compute all the correlation functions of our anyon fields and study an anyonic W-algebra of unbounded operators with a common dense domain. This algebra contains an operator with peculiar exchange relations with the anyon fields. This operator can be interpreted as a second quantised Calogero-Sutherland (CS) Hamiltonian and may be used to solve the CS model. In particular, we inductively construct all eigenfunctions of the CS model from anyon correlation functions, for all particle numbers and positive couplings.