Abstract
Simple two-dimensional models with massless and massive fermions are studied in the Hamiltonian framework. While the ultimate purpose of this study is a comparison between correlation functions constructed from known operator solutions in both space-like and light-front forms of the theory, the main goal at the present stage is to find physical vacuum states of the space-like models as the lowest energy eigenstates of H 0 + H int . This can be accomplished, using Klaiber's bosonization of the vector current, by means of a Bogoliubov transformation of the Hamiltonian which is quadratic in effective boson operators composed of fermion bilinears. The massless Thirring model is studied in this way and recent claims about its broken phase are critically examined. A brief discussion of the physical content of the models with derivative coupling is also included.
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