  We construct transformations that decouple fermionic fields in interaction
with a gauge field, in the path integral representation of the generating
functional. Those transformations express the original fermionic fields in
terms of non-interacting ones, through non-local functionals depending on the
gauge field. This procedure, holding true in any number of spacetime dimensions
both in the Abelian and non-Abelian cases, is then applied to the path integral
bosonization of the Thirring model in 3 dimensions. Knowledge of the decoupling
transformations allows us, contrarily to previous bosonizations, to obtain the
bosonization with an explicit expression of the fermion fields in terms of
bosonic ones and free fermionic fields. We also explain the relation between
our technique, in the two dimensional case, and the usual decoupling in 2
dimensions.
