  The coupled kinetic equation for density and spin Wigner functions are
derived including spin-orbit coupling, electric and magnetic field as well as
selfconsistent Hartree meanfields suited for SU(2) transport. The interactions
are assumed to be with scalar and magnetic impurities as well as scalar and
spin-flip potentials among the particles. The spin-orbit interaction is used in
a form suitable to solid state physics with Rashba or Dresselhaus coupling,
graphene, extrinsic spin-orbit coupling as well as effective nuclear matter
coupling. The deficiencies of the two-fluid model are worked out consisting in
the appearance of an effective in-medium spin-precession. The stationary
solution of all these systems shows a band splitting controlled by an effective
medium-dependent Zeeman field. The selfconsistent precession direction is
discussed and a cancellation of linear spin-orbit coupling at zero temperature
is reported. The precession of spin around this effective direction caused by
spin-orbit coupling leads to anomalous charge and spin currents in an electric
field. Anomalous Hall conductivity is shown to consists of the known results
obtained from Kubo formula or Berry phases and a new symmetric part interpreted
as inverse Hall effect. Analogously the spin-Hall and inverse spin-Hall effect
of spin currents are discussed which are present even without magnetic fields
showing a spin accumulation triggered by currents. The analytical dynamical
expressions for zero temperature are derived and discussed in dependence on the
magnetic field and effective magnetizations. The anomalous Hall and spin-Hall
effect changes sign at higher than a critical frequency dependent on the
relaxation time.
