Equal-time kinetic equations in a rotational field

We investigate quantum kinetic theory for a massive fermion system under a rotational field. From the Dirac equation in curved space we derive the complete set of kinetic equations for the spin components of the covariant and equal-time Wigner functions. While the particles are no longer on a mass shell in general case due to the rotation-spin coupling, there are always only two independent components, which can be taken as the number and spin densities. With the help from the off-shell constraint we obtain the closed transport equations for the two independent components in classical limit and at quantum level. The classical rotation-orbital coupling controls the dynamical evolution of the number density, but the quantum rotation-spin coupling explicitly changes the spin density.