  Here we address the problem of bosonizing massive fermions without making
expansions in the fermion masses in both massive $QED_2$ and $QED_3$ with $ N $
fermion flavors including also a Thirring coupling. We start from two point
correlators involving the U(1) fermionic current and the gauge field.
  From the tensor structure of those correlators we prove that the U(1) current
must be identically conserved (topological) in the corresponding bosonized
theory both in D=2 and D=3 dimensions. We find an effective generating
functional in terms of bosonic fields which reproduces those two point
correlators and from that we obtain a map of the Lagrangian density
$\bar{\psi}^{r} (i \partial / - m){\psi}^{r}$ into a bosonic one in both
dimensions. This map is nonlocal but it is independent of the eletromagnetic
and Thirring couplings, at least in the quadratic approximation for the
fermionic determinant.
