  We study the problem of decoupling fermion fields in 1+1 and 2+1 dimensions,
in interaction with a gauge field, by performing local transformations of the
fermions in the functional integral. This could always be done if singular
(large) gauge transformations were allowed, since any gauge field configuration
may be represented as a singular pure gauge field. However, the effect of a
singular gauge transformation of the fermions is equivalent to the one of a
regular transformation with a non-trivial action on the spinorial indices. For
example, in the two dimensional case, singular gauge transformations lead
naturally to chiral transformations, and hence to the usual decoupling
mechanism based on Fujikawa Jacobians. In 2+1 dimensions, using the same
procedure, different transformations emerge, which also give rise to Fujikawa
Jacobians. We apply this idea to obtain the v.e.v of the fermionic current in a
background field, in terms of the Jacobian for an infinitesimal decoupling
transformation, finding the parity violating result.
