Geodesic
Method of approximate calculating path integrals by using perturbation theory with convergent series. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 51-59 
V. V. Belokurov; Yu. P. Solov'ev; E. T. Shavgulidze. Method of approximate calculating path integrals by using perturbation theory with convergent series. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 1, pp. 51-59. http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a4/
@article{TMF_1996_109_1_a4,
     author = {V. V. Belokurov and Yu. P. Solov'ev and E. T. Shavgulidze},
     title = {Method of approximate calculating path integrals by using perturbation theory with convergent {series.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {51--59},
     year = {1996},
     volume = {109},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a4/}
}
TY  - JOUR
AU  - V. V. Belokurov
AU  - Yu. P. Solov'ev
AU  - E. T. Shavgulidze
TI  - Method of approximate calculating path integrals by using perturbation theory with convergent series. I
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 51
EP  - 59
VL  - 109
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a4/
LA  - ru
ID  - TMF_1996_109_1_a4
ER  - 
%0 Journal Article
%A V. V. Belokurov
%A Yu. P. Solov'ev
%A E. T. Shavgulidze
%T Method of approximate calculating path integrals by using perturbation theory with convergent series. I
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 51-59
%V 109
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1996_109_1_a4/
%G ru
%F TMF_1996_109_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose a method of calculating path integrals according to which the value of integral can be approximated with any given accuracy by the partial sum of a certain absolutely convergent series.

[1] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, 4 izd., Nauka, M., 1984 | MR

[2] Large-order behaviour of perturbation theory, eds. J.-C. le Guillou, J. Zinn-Justin, North-Holland, Amsterdam, 1990

[3] D. I. Kazakov, D. V. Shirkov, Fortschr. Phys., 28 (1980), 465 | DOI | MR

[4] V. V. Kozlov, Simmetrii, topologiya i rezonansy v gamiltonovoi mekhanike, Izd-vo Udm. GU, Izhevsk, 1995 | MR | Zbl

[5] R. B. Dingle, Asymptotic expansions: their derivation and interpretation, Academic Press, London–New York, 1973 | MR | Zbl

[6] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1962, formula (3.469) ; формула (3.462) | MR

[7] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968 | MR | Zbl

[8] O. G. Smolyanov, E. T. Shavgulidze, Kontinualnye integraly, Izd-vo MGU, M., 1990 | MR | Zbl

[9] D. I. Kazakov, A. I. Onischenko, gotovitsya k pechati