Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory

TL;DR

This paper derives a relativistic Boltzmann equation for massive spin-1/2 particles, incorporating nonlocal collision terms and quantum effects, to better understand spin polarization phenomena in high-energy and condensed matter physics.

Contribution

It introduces a quantum field theory-based derivation of the nonlocal collision kernel for spin-1/2 particles within the Wigner-function formalism, including spin degrees of freedom.

Findings

Collision kernel contains local and nonlocal terms at next-to-leading order in 7.

Off-shell contributions cancel out in the Boltzmann equation.

Framework applicable to spin polarization phenomena in heavy-ion collisions and condensed matter systems.

Abstract

We derive the Boltzmann equation and the collision kernel for massive spin-1/2 particles, using the Wigner-function formalism and employing an expansion in powers of $\hbar$. The phase space is enlarged to include a variable related to the spin degrees of freedom. This allows to reduce the transport equations of the independent components of the Wigner function to one scalar equation. To next-to-leading order in $\hbar$, we find that the collision kernel contains both local and nonlocal terms. We show that off-shell contributions cancel in the Boltzmann equation. Our framework can be used to study spin-polarization phenomena induced by vorticity as recently observed in heavy-ion collisions and in condensed-matter systems.