Phase-space descriptions of operators and the Wigner distribution in quantum mechanics I. A Dirac inspired view

TL;DR

This paper introduces a new, efficient phase space framework for quantum operators and the Wigner distribution inspired by Dirac's ideas, with potential for broad generalizations beyond Cartesian spaces.

Contribution

It presents a novel, natural approach to phase space in quantum mechanics inspired by Dirac, enabling extensions to non-Cartesian configuration spaces.

Findings

New phase space description of quantum operators and Wigner distribution

Framework is natural, economical, and extendable to non-Cartesian spaces

Potential for broad generalizations in quantum phase space analysis

Abstract

Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is marked by its economy, naturalness and more importantly, by its potential for extensions and generalisations to situations where the underlying configuration space is non Cartesian.