Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> particles from quantum field theory

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 $\ensuremath{\hbar}$. The phase space is enlarged to include a variable related to the spin degrees of freedom. This allows us to reduce the transport equations of the independent components of the Wigner function to one scalar equation. To next-to-leading order in $\ensuremath{\hbar}$, 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.