Hamiltonian formulation of exactly solvable models and their physical vacuum states

We study simple two-dimensional models with massless and massive fermions in the Hamiltonian framework. While our ultimate goal is to gain a deeper insight to structural differences between the usual (“spacelike” - SL) and light-front (LF) forms of the relativistic dynamics, an attempt is also made to clarify a few conceptual problems of quantum field theory. We point out that contrary to the assumption of canonical quantization, interacting Heisenberg fields do not always reduce to free fields at t=0. We also show that by incorporating operator solutions of the field equations to the canonical formalism, SL and LF Hamiltonians of the derivative-coupling model as well as of the Federbush model acquire an equivalent structure. In the usual canonical treatment, physical predictions in the two schemes disagree - the SL Hamiltonians contain interaction terms while their LF counterparts do not. Using a Bogoliubov transformation, the physical vacuum of the Thirring model is then derived for the first time. It has a form of a coherent state quadratic in composite boson operators which, after bosonization of the vector current, are present in the (nondiagonal) interaction Hamiltonian. To find the vacuum of the Federbush model by an analogous Bogoliubov transformation, we propose a massive version of Klaiberʼs current bosonization and demonstrate advantages of the LF treatment of the model.