Trajectories and spin motion of massive spin-1/2 particles in gravitational fields

From covariant Dirac theory in curved space-time, dynamical equations for the motion of the spin and the spin-induced non-geodesic behaviour of the particle trajectories are deduced. This is done for arbitrary space-times in a generally covariant and observer-independent way. The procedure is thereby based on a WKB scheme and a Gordon decomposition of the Dirac probability four-current. A complete correspondence between the quantum mechanical equations of motion and the classical equations for extended isolated bodies or pole-dipole particles is found. This can as well be taken as a confirmation that to the first order of a WKB approximation the gyro-gravitational factors of the classical angular momentum and of the intrinsic quantum mechanical spin agree.