Quantum–classical correspondence via a deformed kinetic operator

Abstract

We propose an approach to the quantum-classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and kinetic operators which, in addition to the standard quantum expressions, contain terms that are functionals of the N-particle density. We show that this implementation of the quantum-classical correspondence is related to Witten's deformation of the exterior derivative and Laplacian, introduced in the context of supersymmetric quantum mechanics. The corresponding deformed action is also shown to be related to the Fisher information. Finally, we briefly consider the possible relevance of our approach to the construction of kinetic-energy density functionals.