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TMF, 1978, Volume 36, Number 2, Pages 271–278 (Mi tmf4306)  

This article is cited in 11 scientific papers (total in 11 papers)

Methods of calculating many-loop diagrams and renormalization-group analysis of the $\varphi^4$ theory

A. A. Vladimirov


Abstract: An effective technique is developed for calculating the renormalization-group parameters; this makes it possible to set all external momenta equal to zero in the calculation of diagrams. Three- and four-loop calculations of the Gell-Mann–Low function of the $\varphi^4$ theory are made in different renormalization schemes. The dependence of this function on the particular choice of fixed ratios of the momentum arguments of the invariant charge is investigated.

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English version:
Theoretical and Mathematical Physics, 1978, 36:2, 732–737

Bibliographic databases:

Received: 29.12.1977

Citation: A. A. Vladimirov, “Methods of calculating many-loop diagrams and renormalization-group analysis of the $\varphi^4$ theory”, TMF, 36:2 (1978), 271–278; Theoret. and Math. Phys., 36:2 (1978), 732–737

Citation in format AMSBIB
\Bibitem{Vla78}
\by A.~A.~Vladimirov
\paper Methods of calculating many-loop diagrams and renormalization-group analysis of the~$\varphi^4$ theory
\jour TMF
\yr 1978
\vol 36
\issue 2
\pages 271--278
\mathnet{http://mi.mathnet.ru/tmf4306}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=507846}
\transl
\jour Theoret. and Math. Phys.
\yr 1978
\vol 36
\issue 2
\pages 732--737
\crossref{https://doi.org/10.1007/BF01036487}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. I. Kazakov, O. V. Tarasov, D. V. Shirkov, “Analytic continuation of the results of perturbation theory for the model $g\varphi^4$ to the region $g\gtrsim1$”, Theoret. and Math. Phys., 38:1 (1979), 9–16  mathnet  crossref  mathscinet
    2. A. A. Vladimirov, “Method of calculating renormalization-group functions in the scheme of dimensional regularization”, Theoret. and Math. Phys., 43:2 (1980), 417–422  mathnet  crossref  isi
    3. A. N. Vasil'ev, M. Yu. Nalimov, “Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space”, Theoret. and Math. Phys., 55:2 (1983), 423–431  mathnet  crossref  isi
    4. M. Yu. Nalimov, “Regular expansion for calculation of the renormalization-group functions in a theory with dimensional coupling constants”, Theoret. and Math. Phys., 68:2 (1986), 778–788  mathnet  crossref  mathscinet  isi
    5. A. N. Vasil'ev, “Combinatorics of the $R$ operation”, Theoret. and Math. Phys., 81:3 (1989), 1244–1257  mathnet  crossref  mathscinet  isi
    6. M. Reuter, D. Fliegner, M. G. Schmidt, C. Schubert, “Two-loop Euler–Heisenberg lagrangian in dimensional renormalization”, Theoret. and Math. Phys., 113:2 (1997), 1442–1451  mathnet  crossref  crossref  mathscinet  isi
    7. M. V. Komarova, M. Yu. Nalimov, “Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the $(4?\epsilon)$-Dimensionally Regularized $O(n)$-Symmetric $\phi^4$ Theory”, Theoret. and Math. Phys., 126:3 (2001), 339–353  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Schubert, C, “Perturbative quantum field theory in the string-inspired formalism”, Physics Reports-Review Section of Physics Letters, 355:2–3 (2001), 73  isi
    9. Kataev A.L. Mikhailov S.V., “The {?}-expansion formalism in perturbative QCD and its extension”, J. High Energy Phys., 2016, no. 11, 079  crossref  mathscinet  isi  elib  scopus
    10. N. V. Antonov, M. V. Kompaniets, N. M. Lebedev, “Critical behavior of the $O(n)$ $\phi^4$ model with an antisymmetric tensor order parameter: Three-loop approximation”, Theoret. and Math. Phys., 190:2 (2017), 204–216  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. Kompaniets M.V. Panzer E., “Minimally Subtracted Six-Loop Renormalization of O(N)-Symmetric Phi(4) Theory and Critical Exponents”, Phys. Rev. D, 96:3 (2017), 036016  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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