  The Pauli-Poisson equation is a semi-relativistic model for charged
spin-1/2-particles in a strong external magnetic field and a self-consistent
electric potential computed from the Poisson equation in 3 space dimensions. It
is a system of two magnetic Schr\"odinger equations for the two components of
the Pauli 2-spinor, representing the two spin states of a fermion, coupled by
the additional Stern-Gerlach term representing the interaction of magnetic
field and spin.
  We study the global wellposedness in the energy space and the semiclassical
limit of the Pauli-Poisson to the magnetic Vlasov-Poisson equation with Lorentz
force and the semiclassical limit of the linear Pauli equation to the magnetic
Vlasov equation with Lorentz force.
  We use Wigner transforms and a density matrix formulation for mixed states,
extending the work of P. L. Lions & T. Paul as well as P. Markowich & N.J.
Mauser on the semiclassical limit of the non-relativistic Schr\"odinger-Poisson
equation.
