Calogero Model(s) and Deformed Oscillators

TL;DR

This paper reviews recent algebraic and oscillator-based insights into Calogero models, highlighting their emergence from matrix harmonic oscillators and discussing their solvability.

Contribution

It introduces a matrix oscillator framework for Calogero models and explores their algebraic structure and solvability.

Findings

Calogero models can be derived from matrix harmonic oscillators.

The algebraic structure of these models is clarified.

Comments on the models' solvability are provided.

Abstract

We briefly review some recent results concerning algebraical (oscillator) aspects of the $N$-body single-species and multispecies Calogero models in one dimension. We show how these models emerge from the matrix generalization of the harmonic oscillator Hamiltonian. We make some comments on the solvability of these models.