Another Perspective on the Relation Between Classical and Quantum Integrability

Abstract

We describe a framework suggesting how to “deform” in Planck’s constant $h$ the classical concept of integrability. The key point is to use well defined counterparts of Feynman’s measure on the space of paths of the mechanical system. Then we introduce the associated deformation of quantum conservation laws. The method is tested on elementary systems and provide, indeed, more information than expected.