  Within the framework of Weyl calculus we establish a quantum-classical
correspondence for the time evolution of observables generated by a
Dirac-Hamiltonian. This includes a semiclassical separation of particles and
antiparticles. We then prove quantum ergodicity for Dirac-Hamiltonians under
the condition that a skew product of the classical relativistic translational
motion and relativistic spin precession is ergodic.
