Momentum Distribution of a Weakly Coupled Fermi Gas

We apply the sea-boson method to compute the momentum distribution of a spinless continuum Fermi gas in two space dimensions with short-range repulsive interactions. We find that the ground state of the system is a Landau Fermi liquid($ 0 < Z_{F} < 1 $). We also apply this method to study the one-dimensional system when the interactions are long-ranged gauge interactions. We map the Wigner crystal phase of this system.