Remarks on the notion of quantum integrability

TL;DR

This paper examines the concept of quantum integrability, proposing new criteria for classification and discussing the physical properties of models that meet these criteria.

Contribution

It introduces a novel set of criteria for quantum integrability, offering a new classification framework for quantum models.

Findings

Proposes a new classification scheme for quantum integrability.

Links integrability classes to specific physical properties.

Reviews existing definitions and suggests alternative criteria.

Abstract

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.