Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: E(internal) = h(2)Omega C/4 pi am + Sigma(k sigma)(h(2)k(2)/2m)(n(k sigma) - C/k(4)) where the external potential energy is not included, a is the scattering length, Omega is the volume, n(k sigma) is the average number of fermions with wave vector k and spin sigma, and C equivalent to lim(k ->alpha) k(4)n(kl) = lim(k ->infinity)k(4)n(kl). This result is a universal identity. Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including pair correlations and the dimer-fermion scattering length, are also studied. Published by Elsevier Inc.