Consistência no cálculo perturbativo: a eletrodinâmica quântica e a anomalia - Gambin, Ediana (2004)
We use a very general calculational method, concerning the divergences manipulations and calculations, in order to treat the perturbative solution of quantum electrodynamics (QED), at the one loop level, as well as to study the perturbative origin of the axial triangle anomaly related with the electromagnetic decay of the neutral pion. Within the context of the referred method, all one-loop divergent amplitudes are evaluated by taking the most general choices for the routing of internal lines momentum and without assuming an explicit form of regularization in intermediary steps. The expressions for the evaluated Green functions are written in terms of a small set of basic divergent objects and standard one-loop finite structure functions. The relations among Green functions are all verified without any assumption for the involved arbitrariness. A set of conditions, for the consistency in perturbative calculations, is identified by requiring that the evaluated amplitudes become free from ambiguities and symmetry preserving. The renormalization, at the one loop level, is discussed. Adopting then the consistent point of view emerged from the QED analysis we consider the treatment of the axial-vector-vector (AVV) triangle amplitude. As a consequence of our investigations, we can conclude that the traditional way to look at triangle anomalies, based on intrinsic arbitrariness, could be questionable in its role of justifying the perturbative origin of the associated symmetry violations. We show then, by performing exact, analytical and off the mass shell calculations for the involved amplitudes that the anomaly emerges in a natural way and with the correct value for the violations, in the adopted approach, in spite of its nonambiguous character. The advantage of the used strategy, relative to traditional ones, resides in the fact that only one prescription is needed to treat all amplitudes in all theories and models. In addition, the results thus obtained can always be mapped into those corresponding to traditional regularization techniques including the Dimensional Regularization and the surface's terms evaluation approach, providing the specific interpretations of each treatment are adopted for the undefined quantities involved. This means that the consistent QED results of DR as well as the usual surface's term evaluation for the AVV anomaly can be recovered from those obtained within the context of the adopted method but this implies to assume di¤erent values for identical mathematical object. Only the alternative strategy adopted in the present work, to manipulate and calculate the divergences of perturbative solutions of QFT's can give a consistent treatment of both problems in a simultaneous way. Perspectives for additional investigations are pointed out.