Renormalization and Short Distance Singular Structure

Abstract

The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of distributions (and worse defined mathematical objects). Some of them are eliminated defining a multiplication based in dimensional regularization while others disappear considering the states as functionals over the observables space. Non renormalizable theories turn to be finite, but anyhow they are endowed with infinite arbitrary constants.