Divergent Integrals Treatment in Quantum Field Theory

Abstract

This paper presents a brief review on regularization methods and shows that the combination of two techniques could preserve symmetries in all orders of the Perturbation Theory. We will see, with two simple examples in the one-loop-order, what a regularization method needs to preserve symmetries. Furthermore, it will be shown that the problems with symmetry violations by regularization methods are related to the consequences of not being able to simply shift a variable in these divergent integrals. To facilitate the analysis between methods and provide analytical expressions for the finite parts of amplitudes, it was systematized in terms of a set of special functions. In the Appendix we introduce these functions and then cases of specific interest, functions continuity and some useful limits will be presented.