Mathematical renormalization of Hamiltonian field theories

Abstract

We rigorously define renormalized evolution operator of the Schrödinger equation in the infinite dimensional Weyl-Moyal algebra for any time interval for arbitrary Hamiltonian depending on time. We state that for renormalizable field theories, in the interaction representation, and for the time interval being the full real axis, our construction yields standard renormalized $S$-matrix and Green functions of perturbative quantum field theory.

This paper has been withdrawn by the author because the renormalization constructed in it is not compatible with renormalization in perturbative quantum field theory. Main Theorem of \S5 is not true