Anomalias em amplitudes finitas: um cálculo explícito das amplitudes tringulares AVV e AAA em duas dimensões espaço-temporais

Abstract

In this work we present an explicit and detailed investigation concerning the triangular amplitudes axial-vector-vector (AVV) and axial triple (AAA) in two space-time dimensions. These amplitudes are related to the function in two axial-vector points (AV) through contractions with momenta. Due to this fact, before we consider such triangular amplitudes, we establish a point of view for the anomalous amplitude AV. This point of view is constructed within the context in an alternative strategy of manipulation and calculation of Feynman integrals, divergent or not, typical of perturbative solutions of quantum field theories. In the procedure all the amplitudes, in all the theories, formulated in space-time dimensions even or odd, renormalizable or not, are treated in the same way. The ambiguities are automatically eliminated and the relations of simmetry preserved. The well -known anomalous divergent amplitudes are correctly described despite the unambiguous character. After a detailed presentation of all calculations we conclude that the same phenomenon involving the AV amplitude is also present in the finite amplitudes AVV and AAA. This conclusion reinforces the hypothesis that the phenomenon of anomalies is present in all the pseudo amplitudes of a chain of amplitudes where the divergent amplitude AV it is only the simplest structure among them. It is expected that the same will happen in all the dimensions of space time pairs. In particular, in four dimensions, the amplitudes of scattering AVVV and AAAV may display anomalies too.