Degeneracy Structure of the Calogero-Sutherland Model: an Algebraic Approach

TL;DR

This paper explores the degeneracy structure of the Calogero-Sutherland model using algebraic methods, constructing SU(2) operators that connect degenerate eigenstates for multiple particles.

Contribution

It introduces an algebraic framework with explicit SU(2) operators to analyze degeneracies in the Calogero-Sutherland model, generalizing from two to N particles.

Findings

Constructed SU(2) operators for two-particle case

Generalized algebraic operators to N-particle model

Connected degenerate states within eigenspaces

Abstract

The degeneracy structure of the eigenspace of the N-particle Calogero-Sutherland model is studied from an algebraic point of view. Suitable operators satisfying SU(2) algebras and acting on the degenerate eigenspace are explicitly constructed for the two particle case and then appropriately generalized to the N-particle model. The raising and lowering operators of these algebras connect the states, in a subset of the degenerate eigenspace, with each other.