  We address the propagation of the spin along classical trajectories for a
1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing
on classical trajectories as the exact propagation of wave-function
discontinuities we find an explicit spin-transport law for the case of the
Dirac oscillator. In the general case we examine the spin propagation along
classical trajectories emerging as an approximation of the quantum dynamics via
the mechanical analog of the optical eikonal asymptotic approach. Throughout we
establish as many parallels as possible with the equivalent situation for the
electromagnetic field.
