Wigner function for free relativistic particles

TL;DR

This paper generalizes the Wigner function to describe free relativistic particles with the Hamiltonian 1p^2+m^22, providing a phase-space representation for relativistic quantum states.

Contribution

It introduces a novel formulation of the Wigner function specifically adapted for relativistic free particles, extending non-relativistic quantum phase-space methods.

Findings

Derived a relativistic Wigner function expression

Demonstrated consistency with non-relativistic limit

Provided a framework for relativistic quantum state analysis

Abstract

A generalization of the Wigner function for the case of a free particle with the ``relativistic'' Hamiltonian $\sqrt{{\bf p}^2+m^2}$ is given.