On the correspondence between quantum and classical variational principles

TL;DR

This paper demonstrates how classical variational principles can be derived from quantum variational principles through a formal reparameterization, without additional assumptions, illustrating the connection with examples from particle and fluid dynamics.

Contribution

It shows that classical variational principles can be obtained directly from quantum principles without extra assumptions, clarifying their fundamental relationship.

Findings

Classical variational principles can be derived from quantum ones via reparameterization.

Examples include variational formulations for point-particle and fluid motion.

The approach applies to Schrödinger, Pauli, and Klein-Gordon particles.

Abstract

Classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and Klein-Gordon particles.