A New Approach to Renormalization, Using Zeta regularization

Abstract

In this paper we present a method to deal with divergences in perturbation theory using the method of the Zeta regularization, first of all we use the Euler-Mc Laurin Sum formula to associate the divergent integral to a divergent sum in the form 1+2^{m}+3^{m}+... After that we find a recurrence formula for the integrals and apply zeta regularization techniques to obtain finite results for the divergent series. (Through all the paper we use the notation m, for the power of the modulus of p, so we must not confuse it with the value of the mass of the quantum particle) changes: added Bibliography about ramanujan Resummation and references of Zeta regularization in Hardy,s Book "divergent series".