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We clarify a few conceptual problems of quantum field theory on the level ofexactly solvable models with fermions. The ultimate goal of our study is togain a deeper understanding of differences between the usual ("spacelike") andlight-front forms of relativistic dynamics. We show that by incorporatingsolutions of the operator field equations to the canonical formalism thespacelike and light front Hamiltonians of the derivative-coupling model acquirean equivalent structure. The same is true for the massive solvable theory, theFederbush model. In the conventional approach, the physical predictions in thetwo schemes disagree. Moreover, the derivative-coupling model is found to bealmost identical to a free theory, in contrast to the conventional canonicaltreatment. Physical vacuum state of the Thirring model is then obtained by aBogoliubov transformation as a coherent state quadratic in composite bosonoperators. To perform the same task in the Federbush model, we derive a massiveversion of Klaiber's bosonization and show that its light-front form is muchsimpler.

Hamiltonian formulation of exactly solvable models and their physical vacuum states