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Trudy Mat. Inst. Steklova, 2004, Volume 245, Pages 288–295 (Mi tm195)  

This article is cited in 3 scientific papers (total in 3 papers)

Renormalization in Quantum Electrodynamics and Hopf Algebras

I. V. Volovich, D. V. Prokhorenko

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Recently, A. Connes and D. Kreimer introduced the Hopf algebra structure on Feynman graphs in scalar quantum field theory and show that the renormalization can be reduced to the solution of the Riemann–Hilbert problem. In this paper, we suggest a generalization of their construction to the case of quantum electrodynamics. Moreover, we define the action of a gauge group on the Hopf algebra of Feynman diagrams and clarify how this action interacts with the Hopf algebra structure.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 245, 273–280

Bibliographic databases:
Received in February 2004

Citation: I. V. Volovich, D. V. Prokhorenko, “Renormalization in Quantum Electrodynamics and Hopf Algebras”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 245, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 288–295; Proc. Steklov Inst. Math., 245 (2004), 273–280

Citation in format AMSBIB
\Bibitem{VolPro04}
\by I.~V.~Volovich, D.~V.~Prokhorenko
\paper Renormalization in Quantum Electrodynamics and Hopf Algebras
\inbook Selected topics of $p$-adic mathematical physics and analysis
\bookinfo Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov
\serial Trudy Mat. Inst. Steklova
\yr 2004
\vol 245
\pages 288--295
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm195}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099891}
\zmath{https://zbmath.org/?q=an:1181.81091}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 245
\pages 273--280


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Van Suijlekom W.D., “The Hopf algebra of Feynman graphs in quantum electrodynamics”, Lett. Math. Phys., 77:3 (2006), 265–281  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. A. Yu. Morozov, M. N. Serbin, “Nonlinear algebra and Bogoliubov's recursion”, Theoret. and Math. Phys., 154:2 (2008), 270–293  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Bergbauer Ch., Kreimer D., “New Algebraic Aspects of Perturbative and Non-perturbative Quantum Field Theory”, New Trends in Mathematical Physics, 2009, 45–58  crossref  zmath  isi
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