Mathematical Renormalization in Quantum Electrodynamics via Noncommutative Generating Series
DOI10.1007/978-3-319-56932-1_6zbMath1386.81144arXiv1702.08550OpenAlexW2594436735MaRDI QIDQ4609999
V. Hoang Ngoc Minh, Pierre Simonnet, Ngo Quoc Hoan, Gérard H. E. Duchamp, Karol A. Penson
Publication date: 5 April 2018
Published in: Applications of Computer Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1702.08550
nonlinear differential equationsLyndon wordsmonoidal factorizationbases in dualitydivergent polyzetas
Exact enumeration problems, generating functions (05A15) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Applications of Lie (super)algebras to physics, etc. (17B81) Electromagnetic interaction; quantum electrodynamics (81V10) Lasers, masers, optical bistability, nonlinear optics (78A60) Polynomials, factorization in commutative rings (13P05) Polylogarithms and relations with (K)-theory (11G55)
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Cites Work
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- On a conjecture by Pierre Cartier about a group of associators
- Lie elements and an algebra associated with shuffles
- Realisation locale des systèmes non linéaires, algèbres de Lie filtrees transitives et séries generatrices non commutatives
- Vers une notion de dérivation fonctionnelle causale. (Towards a notion of causal functional derivatives)
- Multiple harmonic series
- Matrices de Hankel
- Free Lie algebras and free monoids. Bases of free Lie algebras and factorizations of free monoids
- A natural ring basis for the shuffle algebra and an application to group schemes
- Hopf algebras, renormalization and noncommutative geometry
- Multiple polylogarithms, cyclotomy and modular complexes
- A rationality criterion coming from noncommutative geometry
- The algebra of multiple harmonic series
- Dirichlet functions of order \(n\) and parameter \(t\)
- Summations of polylogarithms via Evaluation transform.
- Shuffle algebra and polylogarithms
- (Pure) transcendence bases in \(\varphi\)-deformed shuffle bialgebras
- Symbolic integration of meromorphic differential systems via Dirichlet functions.
- Combinatorial aspects of polylogarithms and Euler-Zagier sums
- Lyndon words, polylogarithms and the Riemann \(\zeta\) function
- Structure of polyzetas and Lyndon words
- Théorie géométrique des polynômes eulériens
- Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics
- On the definition of a family of automata
- Fonctionnelles causales non linéaires et indéterminées non commutatives
- Iterated path integrals
- Quantum field theory of partitions
- Special values of multiple polylogarithms
- Sch\"utzenberger's factorization on the (completed) Hopf algebra of $q-$stuffle product
- Harmonic sums and polylogarithms at negative multi-indices
- Kontsevich’s integral for the Kauffman polynomial
- The Radiation Theories of Tomonaga, Schwinger, and Feynman
- Free differential calculus. IV: The quotient groups of the lower central series
- From the algebras of Riemann polyzetas to the algebra of Hurwitz polyzetas
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