  It is shown that a useful relativistic generalization of the conventional
spin density for the case of moving electrons is the expectation value of the
four-component Bargmann-Wigner polarization operator. An exact equation of
motion for this quantity is derived, using the one-particle Dirac equation, and
the relativistic analogues of the non-relativistic concepts of spin-currents
and spin-transfer torques are identified. In the classical limit the time
evolution is governed by the equation of motion first proposed by Bargmann,
Michel and Telegdi generalized to the case of inhomogeneous systems. In the
non-relativistic limit it is found that the spin-current has an intrinsic Hall
contribution and to order 1/c^2 a spin-orbit coupling related torque appears in
the equation of motion. The relevance of these results to the theory of the
intrinsic spin Hall effect and current-induced switching are briefly discussed.
