A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction

We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. [J. Math. Pures Appl. 82(6): 665-683, 2003] to the case of unbounded interaction potentials. We also express the mean-field limit as a superhamiltonian system, and state our main result in terms of the Heisenberg-picture dynamics of observables. This is a Egorov-type theorem.