  In this paper we calculate properties of the three-dimensional system of N
species of fermions at zero temperature and finite chemical potential, with the
four-fermionic interaction of the Thirring type. We observe that this model
fits consistently into framework of the Landau Fermi liquid theory, and
possesses a non-trivial zeroth and first Landau parameters. Our result is
derived to all orders of the Thirring coupling constant and to the leading
order of the large-N expansion. In particular we solve for the exact
current-current correlation function, and show that it exhibits a singular
behavior at zero frequency and twice of the Fermi momentum.
