  There exist local infinitesimal redefinitions of the fermionic fields, which
may be used to modify the strength of the coupling for the interaction term in
massless QED3. Under those (formally unitary) transformations, the functional
integration measure changes by an anomalous Jacobian, which (after
regularization) yields a term with the same structure as the quadratic
parity-conserving term in the effective action. Besides, the Dirac operator is
affected by the introduction of new terms, apart from the modification in the
minimal coupling term. We show that the result coming from the Jacobian, plus
the effect of those new terms, add up to reproduce the exact quadratic term in
the effective action. Finally, we also write down the form a finite decoupling
transformation would have, and comment on the unlikelihood of that
transformation to yield a helpful answer to the non-perturbative evaluation of
the fermionic determinant.

High Energy Physics - Theory