  We clarify a few conceptual problems of quantum field theory on the level of
exactly solvable models with fermions. The ultimate goal of our study is to
gain a deeper understanding of differences between the usual ("spacelike") and
light-front forms of relativistic dynamics. We show that by incorporating
solutions of the operator field equations to the canonical formalism the
spacelike and light front Hamiltonians of the derivative-coupling model acquire
an equivalent structure. The same is true for the massive solvable theory, the
Federbush model. In the conventional approach, the physical predictions in the
two schemes disagree. Moreover, the derivative-coupling model is found to be
almost identical to a free theory, in contrast to the conventional canonical
treatment. Physical vacuum state of the Thirring model is then obtained by a
Bogoliubov transformation as a coherent state quadratic in composite boson
operators. To perform the same task in the Federbush model, we derive a massive
version of Klaiber's bosonization and show that its light-front form is much
simpler.
