Mapping the Calogero model on the Anyon model

TL;DR

This paper presents an explicit mapping between the one-dimensional Calogero model and the two-dimensional anyon model, connecting their eigenstates through a convolution kernel based on scattering states.

Contribution

It introduces a novel explicit mapping between Calogero and anyon eigenstates using a convolution kernel derived from scattering eigenstates.

Findings

Successfully maps Calogero eigenstates to anyon eigenstates in a harmonic well

Uses scattering eigenstates to construct the convolution kernel

Provides a new analytical tool for studying Calogero-anyon correspondence

Abstract

We explicitly map the N-body one dimensional Calogero eigenstates in a harmonic well to the lowest Landau level sector of N-body eigenstates of the two dimensional anyon model in a harmonic well. The mapping is achieved in terms of a convolution kernel that uses as input the scattering eigenstates of the free Calogero model on the infinite line, which are obtained in an operator formulation.