Consistência no cálculo perturbativo tridimensional em teoria quântica de campos: a eletrodinâmica quântica

Abstract

In this work we present a detailed study about the three-dimensional quantum electro- dynamics QED3, in perturbative solution at the one loop level. A very general method, concerning the manipulations and calculations involving divergent Feynman integrals, alternative to the traditional regularization techniques, is adopted. The basic physical processes are treated by taking the most general choices for the routing of the internal momenta. The arbitrariness intrinsic to the calculations are preserved in the intermedi- ary operations since that, in fact, the calculation of the divergent integrals is avoided. In order to justify the manipulations performed it is only assumed the presence of a regu- lating distribution in an implicit way. Through the analysis of consistency constraints, constituted by relations among green functions, symmetry relations and determinations of very general theorems, we nd a consistency relation, in the form of a di¤erence between two integrals having the same divergence degree, which reveals necessary and su¢ cient for the desired consistency within the context of three-dimensional perturbative calcula- tions. As a consequence, we have observed that the Lorentz structure of the pure QED3 photon propagator is modi ed by the one loop corrections, in an unavoidable and non ambiguous way, through the induction of a Chern-Simons term in the one loop vacuum polarization tensor calculation, whose implication is the dynamical mass generation for the photon. A systematization for the nite mathematical structures of the perturba- tive three-dimensional one loop calculation is also presented. Such organization play a crucial role in the required mathematical operations involved in the construction of the amplitudes as well for the studies of their symmetry properties.