  While Hartree-Fock theory is well established as a fundamental approximation
for interacting fermions, it has been unclear how to describe corrections to it
due to many-body correlations. In this paper we start from the Hartree-Fock
state given by plane waves and introduce collective particle-hole pair
excitations. These pairs can be approximately described by a bosonic quadratic
Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a
rigorous Gell-Mann-Brueckner-type upper bound to the ground state energy. Our
result justifies the random phase approximation in the mean-field scaling
regime, for repulsive, regular interaction potentials.
