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The behavior of spin-1/2 particle in a weak static gravitational field isconsidered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysentransformation providing also the simple form for the momentum and spinpolarization operators. The operator equations of momentum and spin motion arederived for a first time. Their semiclassical limit is analyzed. The dipolespin-gravity coupling in the previously found (another) Hamiltonian does notlead to any observable effects. The general agreement between the quantum andclassical analysis is established, contrary to several recent claims. Theexpression for gravitational Stern-Gerlach force is derived. The helicityevolution in the gravitational field and corresponding accelerated framecoincides, being the manifestation of the equivalence principle.Comment: 8 pages, no figures; version to appear in Physical Review

Semiclassical limit for Dirac particles interacting with a gravitational field