Simetria de Bose em amplitudes quirais anômalas e aspectos da renormalização da eletrodinâmica quântica reduzida

Abstract

In this thesis we present results on two topics in the context of regularization of gauge theories,thefirstoneontheBosesymmetryinanomalouschiralamplitudesandthesecond one on the renormalization until the two-loop order of reduced quantum electrodynamics. IntheapparentinconsistencyofBosesymmetryinamplitudesrelatedtothechiralanomaly, the preservation of this symmetry leads to fixing the anomaly on the Ward identities, which violates, for example, the conservation of vectorial current. Although this problem is often assumed to be intrinsic to the anomaly itself, we show that it results from the difficulty on how to work with γ5 during the regularization procedure. We demonstrate how to obtain the quantum breaking of Ward identities in a way that allows preserving Bose symmetry independently of the chiral anomaly, in a fixed-dimension method. The results are an evidence of the necessity of a proper prescription on γ5 treatment even in this kind of method. The results on the second topic emerge from the study of the regularization and renormalization of reduced quantum electrodynamics, an effective model to describe fermionic fields restricted to dimensions smaller than that of the gauge fields. In the variants of this model with massless fermions on 1+1 and 2+1 dimensions, we investigate the divergence structure at the one-loop order, where we analyze the relationship with finite arbitrary terms, momentum routing invariance and gauge symmetry. Lastly, we calculate the renormalization constants for massless fermions on 2+1 dimensions at two-loop order.