  We study a few two-dimensional models with massive and massless fermions in
the hamiltonian framework and in both conventional and light-front forms of
field theory. The new ingredient is a modification of the canonical procedure
by taking into account solutions of the operator field equations. After
summarizing the main results for the derivative-coupling and the Thirring
models, we briefly compare conventional and light-front versions of the
Federbush model including the massive current bosonization and a Bogoliubov
transformation to diagonalize the Hamiltonian. Then we sketch an extension of
our hamiltonian approach to the two-dimensional Nambu--Jona-Lasinio model and
the Thirring--Wess models. Finally, we discuss the Schwinger model in a
covariant gauge. In particular, we point out that the solution due to
Lowenstein and Swieca implies the physical vacuum in terms of a coherent state
of massive scalar field and suggest a new formulation of the model's vacuum
degeneracy.
