Nonlinear algebra and Bogoliubov’s recursion

2007/03/28 by A. Morozov, Andrew Morozov, Maksym Serbyn +1 · 12 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Algorithm #Class (philosophy) #Computer science #Geometry #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quadratic equation #Quantum #Quantum field theory #Quantum mechanics #Recursion (computer science) #Renormalization #hep-th

paper · pdf · doi:10.1007/s11232-008-0026-7

published in Theoretical and Mathematical Physics 154(2), 270-293 (Pleiades Publishing) · LaTex, 21 pages

arxiv created 2007/03/28 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Numerous examples are given of application of Bogolubov's forest formula to iterative solutions of various non-linear equations: one and the same formula describes everything, from ordinary quadratic equation to renormalization in quantum field theory.

Citations

• Renormalizable Expansion for Nonrenormalizable Theories: II. Gauge Higher Dimensional Theories
• Non RG logarithms via RG equations
• Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder
• The Hopf Algebra of Feynman Graphs in Quantum Electrodynamics
• Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem
• Renormalizable Expansion for Nonrenormalizable Theories: I. Scalar Higher Dimensional Theories

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