Catálogo de publicaciones - libros

This is the first Barnes lemma:

In this appendix, the analysis of convergence of Feynman integrals based on the alpha representation is briefly described. The UV divergences come from the region of small values of the α-parameters in (2.36), while the off-shell IR divergences arise from the integration over large –. To reveal these divergences, the integration region is divided into so-called ‘sectors’, where new integration variables are introduced, with the goal to obtain a factorization of the integrand. Then the analysis of convergence reduces to power counting in one-dimensional integrals.

In this appendix, some methods which were not considered in Chaps. 3–7 are briefly reviewed. The method based on dispersion relations was successfully used from the early days of quantum field theory. The Gegenbauer Polynomial -Space Technique [13], the method of gluing [15] and the method based on star-triangle uniqueness relations [16, 23, 36] are methods for evaluating massless diagrams. The method of IR rearrangement [38], also in a generalized version based on the -operation [14, 34], is a method oriented at renormalization-group calculations.