Abstract
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 (2.37), while the off-shell IR divergences arise from the integration over large αl. 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.
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© 2006 Springer
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Smirnov, V.A. (2006). Analysis of Convergence and Sector Decompositions. In: Feynman Integral Calculus. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30611-0_12
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DOI: https://doi.org/10.1007/3-540-30611-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30610-8
Online ISBN: 978-3-540-30611-5
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