Ground State Energy of Dense Gases of Strongly Interacting Fermions

We study the ground state energy of a gas of N fermions confined to a unit box in d dimensions. The particles interact through a two-body potential with strength scaled in an N-dependent way as N(-alpha)v, where alpha is an element of R and v is a function of positive type satisfying a mild regularity assumption. Our focus is on the strongly interacting case alpha<1-2/d. We contrast our result with existing results in the weakly interacting case alpha>1-2/d and the transition happening at the mean-field scaling alpha=1-2/d. Our proof is an adaptation of the bosonization technique used to treat the mean-field case.