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Trudy Matematicheskogo Instituta imeni V.A. 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
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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.
Received in February 2004
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Document Type: Article
Language: Russian
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://mathscinet.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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