On the equivalence between implicit regularization and constrained differential renormalization

Constrained differential renormalization (CDR) and the constrained version of implicit regularization are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods, which have rather distinct bases, have been successfully applied to several calculations, which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum-space procedures of implicit regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to regularized ones.