  We present a microscopic derivation of the generalized Boltzmann and
Eilenberger equations in the presence of non-Abelian gauges, for the case of a
non-relativistic disordered Fermi gas. A unified and symmetric treatment of the
charge $[U(1)]$ and spin $[SU(2)]$ degrees of freedom is achieved. Within this
framework, just as the $U(1)$ Lorentz force generates the Hall effect, so does
its $SU(2)$ counterpart give rise to the spin Hall effect. Considering elastic
and spin-independent disorder we obtain diffusion equations for charge and spin
densities and show how the interplay between an in-plane magnetic field and a
time dependent Rashba term generates in-plane charge currents.
