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 $\hslash$. 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 $\hslash$, 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.

• Received 22 March 2021
• Accepted 11 June 2021

DOI:https://doi.org/10.1103/PhysRevD.104.016022