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TMF, 2008, Volume 154, Number 2, Pages 316–343 (Mi tmf6172)  

This article is cited in 10 scientific papers (total in 10 papers)

Nonlinear algebra and Bogoliubov's recursion

A. Yu. Morozova, M. N. Serbinabcde

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine
c L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
d Moscow Institute of Physics and Technology
e Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi"

Abstract: We give many examples of applying Bogoliubov's forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory.

Keywords: quantum field theory, renormalization, nonlinear algebra

DOI: https://doi.org/10.4213/tmf6172

Full text: PDF file (587 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 154:2, 270–293

Bibliographic databases:

Received: 02.04.2007

Citation: A. Yu. Morozov, M. N. Serbin, “Nonlinear algebra and Bogoliubov's recursion”, TMF, 154:2 (2008), 316–343; Theoret. and Math. Phys., 154:2 (2008), 270–293

Citation in format AMSBIB
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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. Itoyama H., Morozov A., “Boundary ring or a way to construct approximate NG solutions with polygon boundary conditions. II”, Prog. Theor. Phys., 120:2 (2008), 231–287  crossref  zmath  adsnasa  isi  elib  scopus
    2. Itoyama H., Mironov A., Morozov A., “Boundary ring: a way to construct approximate NG solutions with polygon boundary conditions. I. $Z_n$-symmetric configurations”, Nuclear Phys. B, 808:3 (2009), 365–410  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Morozov A., Shakirov Sh., “Introduction to integral discriminants”, Journal of High Energy Physics, 2009, no. 12, 002, 39 pp.  crossref  mathscinet  isi  scopus
    4. Morozov A., Shakirov Sh., “Generation of matrix models by (W)over-cap-operators”, Journal of High Energy Physics, 2009, no. 4, 064  crossref  mathscinet  isi  scopus
    5. A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. Yu. Morozov, Sh. R. Shakirov, “New and old results in resultant theory”, Theoret. and Math. Phys., 163:2 (2010), 587–617  mathnet  crossref  crossref  adsnasa  isi  elib
    7. A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    8. Shojaei-Fard A., “Motivic Dyson-Schwinger Equations”, Int. J. Mod. Phys. A, 28:20 (2013)  crossref  mathscinet  isi  elib  scopus
    9. 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
    10. Itoyama H. Mironov A. Morozov A., “Rainbow Tensor Model With Enhanced Symmetry and Extreme Melonic Dominance”, Phys. Lett. B, 771 (2017), 180–188  crossref  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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