Totally classical Calogero model

TL;DR

This paper interprets the classical Calogero model within the framework of fuzzy spheres, deriving its limiting form as the fuzzy sphere becomes an ordinary sphere, and connects it to large N integrable models.

Contribution

It provides a novel geometric interpretation of the Calogero model using fuzzy spheres and derives its large N limit as an integrable system.

Findings

Calogero Lax matrix as a function on fuzzy sphere

Avan-Talon r-matrix as a function on product of fuzzy spheres

Limiting Lax and r-functions define a large N Calogero model

Abstract

We show that the standard Calogero Lax matrix can be interpreted as a function on the fuzzy sphere and the Avan-Talon r-matrix as a function on the direct product of two fuzzy spheres. We calculate the limiting Lax function and r-function when the fuzzy sphere tends to the ordinary sphere and we show that they define an integrable model interpreted as a large N Calogero model by Bordemann, Hoppe and Theisen.