# Feynman's proof of the commutativity of the Calogero integrals of motion

## TL;DR

This paper presents Feynman's unpublished proof demonstrating the commutativity of the integrals of motion in Calogero models, providing historical context and original manuscript insights.

## Contribution

It offers the first detailed transcript of Feynman's proof and historical background, enriching understanding of integrable models and Feynman's approach.

## Key findings

- Feynman's proof confirms integrals of motion commute in Calogero models.
- Historical analysis of Feynman's work on integrable systems.
- Original manuscript scan provides primary source insight.

## Abstract

During his last year of life Feynman became interested in integrable models. In the course of his study of one dimensional particles with inverse square-type potentials (the Calogero class of models) he came up with a field theory-inspired proof of the commutativity of the integrals of motion of the system, which remained unpublished. I present an exact transcript of the proof together with a scan of the first page of Feynman's original manuscript and some historical background.