The spherical sector of the Calogero model as a reduced matrix model

TL;DR

This paper explores the matrix-model foundation of the spherical sector in the rational Calogero model, introducing a diagrammatic method to derive constants of motion and analyze their algebraic structure.

Contribution

It presents a novel diagrammatic technique for explicitly calculating constants of motion and their Poisson brackets in the Calogero model's spherical sector.

Findings

Derived explicit expressions for constants of motion

Established the Poisson algebra structure of these constants

Provided a systematic method for higher-order calculations

Abstract

We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and calculate their Poisson brackets. In this way we obtain all functionally independent constants of motion to any given order in the momenta. Our technique is related to the valence-bond basis for singlet states.