An optimal upper bound for the dilute Fermi gas in three dimensions

In a system of interacting fermions, the correlation energy is defined as the difference between the energy of the ground state and the one of the free Fermi gas. We consider N interacting spin 1/2 fermions in the dilute regime, i.e., p << 1 where p is the total density of the system. We rigorously derive a first order upper bound for the correlation energy with an optimal error term of the order O(p7/3) in the thermodynamic limit. Moreover, we improve the lower bound estimate with respect to previous results getting an error O(p2+1/5).& COPY