  We consider a local effective model for fermionic low lying excitations in a
metal. Introducing a boson auxiliary field and taking into account that the
most significant interactions between quasiparticles arise for those which are
near a given point on the Fermi surface, we find that the effective
boson-fermion interaction is singular for a spatial dimension d=2. We
regularize the theory and apply the renormalization group method. As we vary
the coupling constant as a function of an energy scale parameter we show that
the model undergoes a non-perturbative regime in which the Fermi liquid theory
is no longer valid.
