Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does n
ot apply. In the present contribution we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.
We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary to determin
e renormalization group functions. Relations between these coefficients of different loop orders are derived.
