  In this paper we analyze a system of N identical quantum particles in a
weak-coupling regime. The time evolution of the Wigner transform of the
one-particle reduced density matrix is represented by means of a perturbative
series. The expansion is obtained upon iterating the Duhamel formula. For short
times, we rigorously prove that a subseries of the latter, converges to the
solution of the Boltzmann equation which is physically relevant in the context.
In particular, we recover the transition rate as it is predicted by Fermi's
Golden Rule. However, we are not able to prove that the quantity neglected
while retaining a subseries of the complete original perturbative expansion,
indeed vanishes in the limit: we only give plausibility arguments in this
direction. The present study holds in any space dimension greater than 2.
