Yukawa coupling of quantum fields in two dimensions. I

A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction termV and soV has the form , but there are no momentum cutoffs inV. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hilbert space.This work was supported in part by the National Science Foundation, GP-6165.