From Kadanoff--Baym to Boltzmann equations for massive spin-1/2 fermions

TL;DR

This paper derives Boltzmann equations for massive spin-1/2 fermions from the Kadanoff--Baym framework, incorporating spin effects and nonlocal collisions, enabling first-principles simulations of spin transport phenomena.

Contribution

It introduces a derivation of matrix-valued Boltzmann equations with nonlocal collision terms for spin-1/2 fermions from the Kadanoff--Baym equations, accounting for spin degrees of freedom.

Findings

Derived Boltzmann equations with spin matrix distributions.

Included nonlocal collision terms at next-to-leading order in .

Facilitates first-principles simulations of spin-vorticity coupling.

Abstract

We derive Boltzmann equations for massive spin-1/2 fermions with local and nonlocal collision terms from the Kadanoff--Baym equation in the Schwinger--Keldysh formalism, properly accounting for the spin degrees of freedom. The Boltzmann equations are expressed in terms of matrix-valued spin distribution functions, which are the building blocks for the quasi-classical parts of the Wigner functions. Nonlocal collision terms appear at next-to-leading order in $\hbar$ and are sources for the polarization part of the matrix-valued spin distribution functions. The Boltzmann equations for the matrix-valued spin distribution functions pave the way for simulating spin-transport processes involving spin-vorticity couplings from first principles.