We prove a rigorous upper bound on the correlation energy of interacting
fermions in the mean-field regime for a wide class of interaction potentials.
Our result covers the Coulomb potential, and in this case we obtain the
analogue of the Gell-Mann−Brueckner formula
c1ρlog(ρ)+c2ρ in the high density limit. We do
this by refining the analysis of our bosonization method to deal with singular
potentials, and to capture the exchange contribution which is absent in the
purely bosonic picture.Comment: 57 page