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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

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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
Related articles on Google Scholar: Russian articles, English articles

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
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. D. I. Kazakov, “A method of summing nonalternating asymptotic series”, Theoret. and Math. Phys., 46:3 (1981), 227–236
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
5. Yu. A. Kubyshin, “Sommerfeld–Watson summation of perturbation series”, Theoret. and Math. Phys., 58:1 (1984), 91–97
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
7. I. L. Solovtsov, D. V. Shirkov, “The analytic approach in quantum chromodynamics”, Theoret. and Math. Phys., 120:3 (1999), 1220–1244
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
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
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
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
12. Prudnikov, VV, “Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model”, Physical Review E, 81:1 (2010), 011130
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
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
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
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
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