Relativistic Wigner function and consistent classical limit for spin 1/2 particles

TL;DR

This paper simplifies the complex equations governing the relativistic Wigner function for spin 1/2 particles into Dirac-type PDEs, enabling easier numerical analysis and a clear classical limit in a covariant framework.

Contribution

It introduces a simplified form of the equations of motion for the relativistic Wigner function, facilitating numerical computation and a consistent classical limit.

Findings

Equations of motion are reduced to Dirac-type PDEs.

The new formulation is well-suited for numerical methods.

A manifestly covariant classical limit is established.

Abstract

The relativistic Wigner function for spin 1/2 particles is the subject of active research due to diverse applications. However, further progress is hindered by the fabulous complexity of the integro-differential equations of motion. We simplify these equations to partial differential equations of the Dirac type that are not only well suited for numerical computation, but also posses a well defined classical limit in a manifestly covariant form.