  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.
