According to a theory of H. Spohn, the time-dependent Hartree (TDH) equation governs the 1-particle state in $N$-particle systems whose dynamics are prescribed by a non-relativistic Schrödinger equation with 2-particle interactions, in the limit $N$ tends to infinity while the strength of the 2-particle interaction potential is scaled by $1=N$. In previous work we have considered the same mean field scaling for systems of fermions, and established that the error of the time-dependent Hartree-Fock (TDHF) approximation tends to 0 as $N$ tends to infinity. In this article we extend our results to systems of fermions with m-particle interactions $(m > 2)$.
"The TDHF Approximation for Hamiltonians with $m$-particle Interaction Potentials." Commun. Math. Sci. 5 (S1) 1 - 9, February 2007.