Correlation energy of a weakly interacting Fermi gas

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