Constructive field theory: Thirring model interaction $(\widetilde\psi\gamma^{\mu}\widetilde\psi)_2^2$. I. Local field

Self-interacting ferrhion field with a zero rest mass in two-dimensional space-time is investigated by methods of the so called constructive field theory. The renormalized Hamiltonian including cut-off formfactors and counter-terms of a definite structure and the Heisenberg field corresponding to this Hamiltonian are constructed. The space of physical particles is explicitly described, in which both the Hamiltonian and the Heisenberg field admit the removal of the ultraviolet eut-off. The Wightman functions corresponding to the local field obtained admit the removal of the spatial cut-off. The form of the counter-terms is found, with which the limit Wightman functions coincide with those constructed by Klaiber.