Mean field dynamics of fermions and the time-dependent Hartree-Fock equation

The time-dependent Hartree-Fock equations are derived from the N-body linear Schrodinger equation with the mean-field scaling in the limit N --> +infinity and for initial data that are close to Slater determinants. Only the case of bounded, symmetric binary interaction potentials is treated in this work. We prove that, as N --> +infinity, the first partial trace of the N-body density operator approaches the solution of the time-dependent Hartree-Fock equations (in operator form) in the sense of the trace norm. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.