Navegando por Autor "Pontes, Carlos Renato"
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Item Implicit regularization beyond one-loop order : scalar field theories.(2007) Pontes, Carlos Renato; Scarpelli, Antônio Paulo Baêta; Sampaio, Marcos Donizeti Rodrigues; Nemes, Maria CarolinaImplicit regularization (IR) has been shown as a useful momentum space tool for perturbative calculations in dimension-specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one-loop level. In this paper, we aim at generalizing systematically IR to be applicable beyond one-loop order. We use a scalar field theory as an example and pave the way for the extension to quantum field theories which are richer from the symmetry content viewpoint. Particularly, we show that a natural (minimal) renormalization scheme emerges, in which the infinities displayed in terms of integrals in one internal momentum are subtracted, whereas infrared and ultraviolet modes do not mix and therefore leave no room for ambiguities. A systematic cancellation of the infrared divergences at any loop order takes place between the ultraviolet finite and divergent parts of the amplitude for non-exceptional momenta leaving, as a by-product, a renormalization group scale.Item On the equivalence between implicit regularization and constrained differential renormalization.(2008) Pontes, Carlos Renato; Scarpelli, Antônio Paulo Baêta; Sampaio, Marcos Donizeti Rodrigues; Fernandes, José Luiz Acebal; Nemes, Maria CarolinaConstrained 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.