Lorentz-covariant nonlocal collision term for spin-1/2 particles

TL;DR

This paper derives a Lorentz-covariant nonlocal collision term for the Boltzmann equation for spin-1/2 particles, ensuring full Lorentz invariance using advanced quantum kinetic approaches.

Contribution

It presents a new derivation that maintains Lorentz covariance of the nonlocal collision term, improving upon previous non-covariant calculations.

Findings

Collision term is fully Lorentz covariant.

Reconciliation of Wigner-function and Kadanoff-Baym approaches.

Enhanced theoretical consistency in relativistic kinetic theory.

Abstract

We revisit the derivation of the nonlocal collision term in the Boltzmann equation for spin-1/2 particles, using both the Wigner-function approach by de Groot, van Leeuwen, and van Weert, and the Kadanoff-Baym equation in $T$-matrix approximation. Contrary to previous calculations, our results maintain full Lorentz covariance of the nonlocal collision term.