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Mathematical renormalization in quantum electrodynamics via noncommutative generating series. (English) Zbl 1386.81144
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 59-100 (2017).
Summary: 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 \(\varphi\)-deformed shuffle algebras. It is a sequel of G. H. E. Duchamp [“(Pure) transcendence bases in \(\varphi\)-deformed shuffle bialgebras”, Preprint, arXiv:1507.01089] 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 \(\{0,1,+\infty \}\).
For the entire collection see [Zbl 1379.13001].

MSC:
81V10 Electromagnetic interaction; quantum electrodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
11G55 Polylogarithms and relations with \(K\)-theory
05A15 Exact enumeration problems, generating functions
13P05 Polynomials, factorization in commutative rings
17B81 Applications of Lie (super)algebras to physics, etc.
78A60 Lasers, masers, optical bistability, nonlinear optics
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