Abstract
The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution:Einternal=ℏ2ΩC/4πam+∑kσ(ℏ2k2/2m)(nkσ-C/k4)where the external potential energy is not included, a is the scattering length, Ω is the volume, nkσ is the average number of fermions with wave vector k and spin σ, and C≡limk→∞k4nk↑=limk→∞k4nk↓. 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.
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