Using the operator formalism, we obtain the bosonic representation for
the free fermion field satisfying an equation of motion with higher-o
rder derivatives. Then, we consider the operator solution of a general
ized Schwinger model with higher-derivative coupling. Since the increa
sing of the derivative order implies the introduction of an equivalent
number of extra fermionic degrees of freedom, the mass acquired by th
e gauge field is bigger than the one for the standard two-dimensional
QED. An analysis of the problem from the functional integration point
of view corroborates the findings of canonical quantization, and corre
cts certain results previously announced in the literature on the basi
s of Fujikawa's technique.