  The classification of the regularization ambiguity of 2D fermionic
determinant in three different classes according to the number of second-class
constraints, including the new faddeevian regularization, is examined and
extended. We found a new and important result that the faddeevian class, with
three second-class constraints, possess a free continuous one parameter family
of elements. The criterion of unitarity restricts the parameter to the same
range found earlier by Jackiw and Rajaraman for the two-constraints class. We
studied the restriction imposed by the interference of right-left modes of the
chiral Schwinger model ($\chi QED_{2}$) using Stone's soldering formalism. The
interference effects between right and left movers, producing the massive
vectorial photon, are shown to constrain the regularization parameter to belong
to the four-constraints class which is the only non-ambiguous class with a
unique regularization parameter.
