Geodesic
Analytic continuation of the results of perturbation theory for the model $g\varphi^4$ to the region $g\gtrsim1$
Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 1, pp. 15-25 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $g\gtrsim1$. 
@article{TMF_1979_38_1_a1,
     author = {D. I. Kazakov and O. V. Tarasov and D. V. Shirkov},
     title = {Analytic continuation of the results of perturbation theory for the model~$g\varphi^4$ to the region~$g\gtrsim1$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {15--25},
     year = {1979},
     volume = {38},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a1/}
}
TY  - JOUR
AU  - D. I. Kazakov
AU  - O. V. Tarasov
AU  - D. V. Shirkov
TI  - Analytic continuation of the results of perturbation theory for the model $g\varphi^4$ to the region $g\gtrsim1$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 15
EP  - 25
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a1/
LA  - ru
ID  - TMF_1979_38_1_a1
ER  - 
%0 Journal Article
%A D. I. Kazakov
%A O. V. Tarasov
%A D. V. Shirkov
%T Analytic continuation of the results of perturbation theory for the model $g\varphi^4$ to the region $g\gtrsim1$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 15-25
%V 38
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a1/
%G ru
%F TMF_1979_38_1_a1
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 $g\gtrsim1$. Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 1, pp. 15-25. http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a1/

[1] G. A. Baker, B. G. Nickel, M. S. Green, D. I. Meiron, Phys. Rev. Lett., 36 (1976), 1351 | DOI

[2] F. M. Dittes, Yu. A. Kubyshin, O. V. Tarasov, Preprint JINR E2-11100, Dubna, 1977; ТМФ, 37 (1978), 66 | MR

[3] A. A. Vladimirov, Preprint JINR E2-11096, Dubna, 1977; ТМФ, 36 (1978), 271

[4] L. N. Lipatov, ZhETF, 72 (1977), 411 | MR

[5] E. Brézin, J.-C. Le Guillon, J. Zinn-Justin, Phys. Rev., D15, 1544; (1977), 1558

[6] A. A. Vladimirov, TMF, 25 (1975), 335

[7] L. N. Lipatov, ZhETF, 71 (1976), 2010 | MR

[8] G. Khardi, Raskhodyaschiesya ryady, IL, 1951

[9] E. B. Bogomolny, Phys. Lett., 67B (1977), 193 | DOI | MR

[10] B. D. Derfel, D. I. Kazakov, D. V. Shirkov, Preprint JINR E2-10720, Dubna, 1977 | Zbl

[11] J. P. Eckmann, J. Magnen, B. Sénéor, Commun. Math. Phys., 39 (1975), 251 | DOI | MR

[12] S. Graffi, V. Grecchi, B. Simon, Phys. Lett., 32B (1970), 631 | DOI | MR

[13] C. A. Truesdell, Ann. of Math., 46 (1945), 114 | MR

[14] J. J. Loeffel, Workshop on Pade approximants, eds. D. Bessis, J. Gilewicz, P. Merry, CEA, 1976 ; E. Brézin, Review Talk, European Particle Physics Conference, Budapest, 1977 | MR

[15] C. Bervillier, J. M. Drouffe, C. Godréche, J. Zinn-Justin, Saclay Preprint DPh T/77/101, 1977

[16] G. V. Efimov, Preprint OIYaI R2-11462, Dubna, 1978

[17] V. S. Popov, V. L. Eletskii, A. V. Turbiner, ZhETF, 74 (1978), 495 | MR

[18] D. V. Shirkov, Lett. Nuovo. Cim., 18 (1977), 452 | DOI

[19] G. Parisi, Phys. Lett., 69B (1977), 329 | DOI