  We analyze the universality of the bosonization rules in non-relativistic
fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic
dispersion relations, a general fermionic theory can be mapped into a gauge
theory in such a way that the fermionic density maps into a magnetic flux and
the fermionic current maps into a transverse electric field. These are
universal rules in the sense that they remain valid whatever the interaction
considered. We also show that these rules are universal in the case of
non-linear dispersion relations provided we consider only density-density
interactions. We apply the functional bosonization formalism to a
non-relativistic and non-local massive Thirring-like model and evaluate the
spectrum of collective excitations in several limits. In the large mass limit,
we are able to exactly calculate this spectrum for arbitrary density-density
and current-current interactions. We also analyze the massless case and show
that it has no collective excitations for any density-density potential in the
Gaussian approximation. Moreover, the presence of current interactions may
induce a gapless mode with a linear dispersion relation.
