Mean-field dynamics of fermions with relativistic dispersion

We extend the derivation of the time-dependent Hartree-Fock equation recently obtained by Benedikter et al. [Mean-field evolution of fermionic systems, Commun. Math. Phys. (to be published)] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the pseudo-relativistic Hartree-Fock evolution. (C) 2014 AIP Publishing LLC.