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

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

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

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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
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
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
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
5. A. N. Vasil'ev, “Combinatorics of the $R$ operation”, Theoret. and Math. Phys., 81:3 (1989), 1244–1257
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
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
8. Schubert, C, “Perturbative quantum field theory in the string-inspired formalism”, Physics Reports-Review Section of Physics Letters, 355:2–3 (2001), 73
9. Kataev A.L. Mikhailov S.V., “The {?}-expansion formalism in perturbative QCD and its extension”, J. High Energy Phys., 2016, no. 11, 079
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
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
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