Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 143, Number 1, Pages 22–32
DOI: https://doi.org/10.4213/tmf1801 (Mi tmf1801) 		 
This article is cited in 5 scientific papers (total in 5 papers)

The Hopf graph algebra and renormalization group equations

D. V. Malyshevabc

a M. V. Lomonosov Moscow State University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c Princeton University
Full-text PDF (226 kB) Citations (5)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf1801
Abstract: We study the renormalization group equations implied by the Hopf graph algebra. The vertex functions are regarded as vectors in the dual space of the Hopf algebra. The renormalization group equations for these vertex functions are equivalent to those for individual Feynman integrals. The solution of the renormalization group equations can be represented in the form of an exponential of the beta function. We clearly show that the exponential of the one-loop beta function allows finding the coefficients of the leading logarithms for individual Feynman integrals. The calculation results agree with those obtained in the parquet approximation.
Keywords: Hopf graph algebra, renormalization group, leading logarithms.
Received: 07.09.2004
English version:
Theoretical and Mathematical Physics, 2005, Volume 143, Issue 1, Pages 505–514
DOI: https://doi.org/10.1007/s11232-005-0086-x
Bibliographic databases:
Language: Russian
Citation: D. V. Malyshev, “The Hopf graph algebra and renormalization group equations”, TMF, 143:1 (2005), 22–32; Theoret. and Math. Phys., 143:1 (2005), 505–514
Citation in format AMSBIB
\Bibitem{Mal05}
\by D.~V.~Malyshev
\paper The Hopf graph algebra and renormalization group equations
\jour TMF
\yr 2005
\vol 143
\issue 1
\pages 22--32
\mathnet{http://mi.mathnet.ru/tmf1801}
\crossref{https://doi.org/10.4213/tmf1801}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2170053}
\zmath{https://zbmath.org/?q=an:1178.81193}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2005TMP...143..505M}
\elib{https://elibrary.ru/item.asp?id=9132043}
\transl
\jour Theoret. and Math. Phys.
\yr 2005
\vol 143
\issue 1
\pages 505--514
\crossref{https://doi.org/10.1007/s11232-005-0086-x}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000229249500003}
Linking options:
  • https://www.mathnet.ru/eng/tmf1801
  • https://doi.org/10.4213/tmf1801
  • https://www.mathnet.ru/eng/tmf/v143/i1/p22
    • This publication is cited in the following 5 articles:
    1. D. V. Millionshchikov, S. V. Smirnov, “Characteristic algebras and integrable exponential systems”, Ufa Math. J., 13:2 (2021), 41–69  mathnet  crossref  isi
    2. M. V. Polyakov, K. M. Semenov-Tian-Shansky, A. O. Smirnov, A. A. Vladimirov, “Quasirenormalizable quantum field theories”, Theoret. and Math. Phys., 200:2 (2019), 1176–1192  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Shojaei-Fard A., “Formal Aspects of Non-Perturbative Quantum Field Theory Via An Operator Theoretic Setting”, Int. J. Geom. Methods Mod. Phys., 16:12 (2019), 1950192  crossref  mathscinet  isi
    4. Shojaei-Fard A., “Counterterms in the Context of the Universal Hopf Algebra of Renormalization”, Int. J. Mod. Phys. A, 29:8 (2014), 1450045  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:568
    Full-text PDF :279
    References:74
    First page:1
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025