  Correct quantum Hamiltonians of a few exactly solvable models in two
space-time dimensions are derived by taking into account operator solutions of
the field equations. While two versions of the model with derivative coupling
are found to be equivalent in many respects to a free theory, physical vacua of
the massless Thirring and Federbush models are obtained by means of a
Bogoliubov transformation in the form of a coherent state quadratic in
composite boson operators. Contrary to the conventional treatment, the
Federbush model is shown to have the same interacting structure in both
space-like and light-front formulations.
