  The mean field limit for systems of many fermions is naturally coupled with a
semiclassical limit. This makes the analysis of the mean field regime much more
involved, compared with bosonic systems. In this paper, we study the dynamics
of initial data close to a Slater determinant, whose reduced one-particle
density is an orthogonal projection $\omega_N$ with the appropriate
semiclassical structure. Assuming some regularity of the interaction potential,
we show that the evolution of such an initial data remains close to a Slater
determinant, with reduced one-particle density given by the solution of the
Hartree-Fock equation with initial data $\omega_N$. Our result holds for all
(semiclassical) times, and gives effective bounds on the rate of the
convergence towards the Hartree-Fock dynamics.
