  We carry out an investigation imposing a chiral constraint in the phase space
of vector and axial-vector Schwinger model. We find that resulting model is
identical to gauge non-invariant model which was obtained by the imposition of
chiral constraint in the phase-space of in Chiral Schwinger model with the
parameter-free Faddeevian anomaly. Three different models having different
types of interaction between the matter and gauge field become
indistinguishable under a chiral constraint at the quantum mechanical level.
The resulting gauge non-invariant model has an equivalent gauge-invariant
version in the same phase space that can be identified with the vector
Schwinger model.
