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TMF, 1979, Volume 38, Number 1, Pages 15–25 (Mi tmf2533)  

This article is cited in 16 scientific papers (total in 16 papers)

Analytic continuation of the results of perturbation theory for the model $g\varphi^4$ to the region $g\gtrsim1$

D. I. Kazakov, O. V. Tarasov, D. V. Shirkov


Abstract: It is considered what new has been achieved by the progress in many-loop calculations and the method of asymptotic estimates of the perturbation series coefficients in the elucidation of the physical situation with regard to the behavior of the effective charg at short distances. The treatment is given for the example of the theory $\varphi^4_{(4)}$. A procedure is proposed for constructing approximants of the Gell-Mann–Low function on the basis of a synthesis of the exact coefficients of the lowest orders and asymptotic estimates in the integral representation. It is shown that in the $g\varphi^4$ model the Gell-Mann–Low function has behavior of the type $0{,}9 g^2$ for $g\gtrsim1$.

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English version:
Theoretical and Mathematical Physics, 1979, 38:1, 9–16

Bibliographic databases:

Received: 30.06.1978

Citation: 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 $g\gtrsim1$”, TMF, 38:1 (1979), 15–25; Theoret. and Math. Phys., 38:1 (1979), 9–16

Citation in format AMSBIB
\Bibitem{KazTarShi79}
\by D.~I.~Kazakov, O.~V.~Tarasov, D.~V.~Shirkov
\paper Analytic continuation of the results of perturbation theory for the model~$g\varphi^4$ to the region~$g\gtrsim1$
\jour TMF
\yr 1979
\vol 38
\issue 1
\pages 15--25
\mathnet{http://mi.mathnet.ru/tmf2533}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=525847}
\transl
\jour Theoret. and Math. Phys.
\yr 1979
\vol 38
\issue 1
\pages 9--16
\crossref{https://doi.org/10.1007/BF01030252}


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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. D. V. Shirkov, “Asymptotic series in quantum-field asymptotics”, Theoret. and Math. Phys., 40:3 (1979), 785–790  mathnet  crossref  isi
    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. D. I. Kazakov, “A method of summing nonalternating asymptotic series”, Theoret. and Math. Phys., 46:3 (1981), 227–236  mathnet  crossref  mathscinet  zmath  isi
    4. Yu. A. Kubyshin, “Corrections to the asymptotic expressions for the higher orders of perturbation theory”, Theoret. and Math. Phys., 57:3 (1983), 1196–1202  mathnet  crossref  mathscinet  isi
    5. Yu. A. Kubyshin, “Sommerfeld–Watson summation of perturbation series”, Theoret. and Math. Phys., 58:1 (1984), 91–97  mathnet  crossref  mathscinet  isi
    6. L. D. Korsun, A. N. Sisakyan, I. L. Solovtsov, “Variational perturbation theory. $\varphi^{2k}$ oscillator”, Theoret. and Math. Phys., 90:1 (1992), 22–34  mathnet  crossref  mathscinet  isi
    7. I. L. Solovtsov, D. V. Shirkov, “The analytic approach in quantum chromodynamics”, Theoret. and Math. Phys., 120:3 (1999), 1220–1244  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Kazakov, DI, “On the summation of divergent perturbation series in quantum mechanics and field theory”, Journal of Experimental and Theoretical Physics, 95:4 (2002), 581  crossref  isi
    9. D. I. Kazakov, V. S. Popov, “Asymptotic behavior of the Gell-Mann-Low function in quantum field theory”, JETP Letters, 77:9 (2003), 453–457  mathnet  crossref
    10. A. S. Krinitsyn, V. V. Prudnikov, P. V. Prudnikov, “Calculations of the dynamical critical exponent using the asymptotic series summation method”, Theoret. and Math. Phys., 147:1 (2006), 561–575  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Prudnikov, VV, “Renormalization-group description of nonequilibrium critical short-time relaxation processes: A three-loop approximation”, Journal of Experimental and Theoretical Physics, 106:6 (2008), 1095  crossref  adsnasa  isi
    12. Prudnikov, VV, “Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model”, Physical Review E, 81:1 (2010), 011130  crossref  isi
    13. Prudnikov V.V., Prudnikov P.V., Kalashnikov I.A., Rychkov M.V., “Nonequilibrium critical relaxation of structurally disordered systems in the short-time regime: Renormalization group description and computer simulation”, Journal of Experimental and Theoretical Physics, 110:2 (2010), 253–264  crossref  isi
    14. 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
    15. 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
    16. Mera H., Pedersen T.G., Nikolic B.K., “Fast Summation of Divergent Series and Resurgent Transseries From Meijer-G Approximants”, Phys. Rev. D, 97:10 (2018), 105027  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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