Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model

TL;DR

This paper derives an exact expression for the hole propagator in the SU(2) Calogero-Sutherland model using Jack polynomials with prescribed symmetry, confirming a previous conjecture and advancing analytical understanding of the model.

Contribution

It provides the first exact formula for the hole propagator at arbitrary coupling, utilizing Jack polynomials with prescribed symmetry, and proves a related conjecture.

Findings

Exact expression for hole propagator obtained

Conjecture about the propagator proved

Method based on Jack polynomials with prescribed symmetry

Abstract

We study the hole propagator of the Calogero-Sutherland model with SU(2) internal symmetry. We obtain the exact expression for arbitrary non-negative integer coupling parameter $\beta$ and prove the conjecture proposed by one of the authors. Our method is based on the theory of the Jack polynomials with a prescribed symmetry.