Asymptotic observables and Coulomb scattering for the Dirac equation

We analyse the long-time behaviour of scattering states for the Dirac equation, in particular propagation properties in phase space. A major tool are the temporal asymptotics of observables like e.g. position, velocity, or the projections to positive/negative kinetic energy. Fairly general potentials of long and of short range are admitted. As a special application we give a simple proof of asymptotic completeness for the relativistic Coulomb system