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We derive Boltzmann equations for massive spin-1/2 fermions with local andnonlocal collision terms from the Kadanoff--Baym equation in theSchwinger--Keldysh formalism, properly accounting for the spin degrees offreedom. The Boltzmann equations are expressed in terms of matrix-valued spindistribution functions, which are the building blocks for the quasi-classicalparts of the Wigner functions. Nonlocal collision terms appear atnext-to-leading order in $\hbar$ and are sources for the polarization part ofthe matrix-valued spin distribution functions. The Boltzmann equations for thematrix-valued spin distribution functions pave the way for simulatingspin-transport processes involving spin-vorticity couplings from firstprinciples.

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