Hamiltonian formulation of the exactly solvable models and their vacuum structure

2010 Proceedings of Light Cone 2010: Relativistic Hadronic and Particle Physics — PoS(LC2010)   unpublished
Simple two-dimensional models with massless and massive fermions are studied within the conventional (spacelike) and light front forms of the hamiltonian dynamics. The ultimate motivation is to understand deeper the relationship between these two formulations of quantum field theory. The models under study include versions of the derivative coupling model (Schroer, Rothe-Stamatescu), the Thirring and the Federbush model. The correct quantum Hamiltonians that incorporate knowledge of the
more » ... solutions of the field equations, are derived. Some previous results are critically examined. While the derivative-coupling model is found to be equivalent in many respects to a free theory, the physical vacuum states of the massless Thirring and Federbush models can be obtained by means of a Bogoliubov transformation in the form of a coherent state quadratic in composite boson operators. The massive version of the Klaiber's current bosonization is constructed in the both space-like and light front forms. The massive Federbush model is shown to have the same interacting structure in the both schemes when the operator solutions are taken into account. We argue that the Federbush model is particularly suitable for a detailed nonperturbative comparison between the two forms of the relativistic dynamics. Light Cone 2010: Relativistic Hadronic and Particle Physics
doi:10.22323/1.119.0025 fatcat:75aqoppxjjahxokq25bjzevz2q