From quantum to classical without Planck constant going to zero

TL;DR

This paper introduces rules to transition from quantum to classical dynamics without zeroing the Planck constant, using averaging over auxiliary variables to connect quantum Moyal and classical Liouville operators.

Contribution

The paper presents a novel method to derive classical evolution from quantum mechanics without the traditional limit of Planck constant approaching zero.

Findings

Established rules for quantum-to-classical transition via averaging.

Demonstrated the connection between Moyal and Liouville operators.

Provided a framework avoiding the zero Planck constant limit.

Abstract

In this paper we put forward some simple rules which can be used to pass from the quantum Moyal evolution operator to the classical Liouville one without taking the Planck constant to zero. These rules involve the averaging over some auxiliary variables.