Generalização do procedimento de regularização implícita para ordens superiores em teorias de calibre abelianas

Abstract

We extend a constrained version of Implicit Regularization (CIR) beyondone loop order for gauge field theories. In this framework, the ultravioletcontent of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward-Slavnov-Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian Gauge Field Theories (scalar and spinorial QED) to two loop order and calculate the two-loop beta-function of the spinorial QED. As a second contribution, we establish a systematization of the calculation of multiloop amplitudes of massless models with Implicit Regularization. We show that the ultraviolet content of such amplitudes have a simple structure and it permits as a byproduct the identification of all the potential symmetry violating terms, the surface terms. Moreover, we develop a technique for the calculation of the finite part of multiloop integrals coming from amplitudes of massless theories in connection with Implicit Regularization (IR). The usual techniques for calculation at a superior order in massless theories are not applicable in the context of IR. We use a well known mathematical identity to express the integrand in an adequate form to use Feynman parametrization. This renders the process of calculation simple and permits the ystematization of the calculus for a typical n-loop integral, with a direct cancelation of the fictitious mass introduced by the procedure of IR.