Dirac Particles in a Gravitational Field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in comparison to previous works on the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings which contribute to the breaking of the particle - antiparticle symmetry.