Correlation energy of a weakly interacting Fermi gas

We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.

Automated summary

In a scaling regime of high density and weak interaction, the leading order of the correlation energy of a Fermi gas was rigorously derived and verified to be in agreement with the prediction of the random-phase approximation. The method of collective bosonization in three dimensions was refined in this proof. The effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state was approximately diagonalized, showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.