Mathematical renormalization in quantum electrodynamics via noncommutative generating series

Abstract

In order to push the study of solutions of nonlinear differential equations involved in quantum electrodynamics (The present work is part of a series of papers devoted to the study of the renormalization of divergent polyzetas (at positive and at negative indices) via the factorization of the non commutative generating series of polylogarithms and of harmonic sums and via the effective construction of pairs of bases in duality in φ -deformed shuffle algebras. It is a sequel of [6] and its content was presented in several seminars and meetings, including the 66th and 74th Séminaire Lotharingien de Combinatoire.), we focus on combinatorial aspects of their renormalization at {0, 1, +∞}.