  General relativistic quantum dynamics of twisted (vortex) Dirac particles is
constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen
representation are derived for a twisted relativistic electron in arbitrary
electric and magnetic fields. A critical experiment for a verification of the
results is proposed. The new important effect of a radiative orbital
polarization of a twisted electron beam in a magnetic field resulting in a
nonzero average projection of the intrinsic orbital angular momentum on the
field direction is predicted.
