Geodesic
On summation of the contributions from the Feynman diagrams. An
Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1005-1025.

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

A method is proposed for the summation of the series of contributions from Feynman diagrams. The proof is given of an existence theorem for the solution of an equation which arises in the summation of series of contributions. 
@article{IM2_1968_2_5_a4,
     author = {D. Ya. Petrina},
     title = {On summation of the contributions from the {Feynman} diagrams. {An}},
     journal = {Izvestiya. Mathematics },
     pages = {1005--1025},
     publisher = {mathdoc},
     volume = {2},
     number = {5},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a4/}
}
TY  - JOUR
AU  - D. Ya. Petrina
TI  - On summation of the contributions from the Feynman diagrams. An
JO  - Izvestiya. Mathematics 
PY  - 1968
SP  - 1005
EP  - 1025
VL  - 2
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a4/
LA  - en
ID  - IM2_1968_2_5_a4
ER  - 
%0 Journal Article
%A D. Ya. Petrina
%T On summation of the contributions from the Feynman diagrams. An
%J Izvestiya. Mathematics 
%D 1968
%P 1005-1025
%V 2
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a4/
%G en
%F IM2_1968_2_5_a4
D. Ya. Petrina. On summation of the contributions from the Feynman diagrams. An. Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1005-1025. http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a4/

[1] Daison F., “$S$-matritsa v kvantovoi elektrodinamike”, Noveishee razvitie kvantovoi elektrodinamiki, Sbornik statei, IL, M., 1954, 205–238

[2] Xardi G., Raskhodyaschiesya ryady, IL, M., 1951

[3] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Gostekhizdat, M., 1957 | MR

[4] Taylor J. G., “On the existence of field theory. I. The analitic approach”, J. Math. Ph., 7:9 (1956), 1720–1729 ; “On the Field Equations”, Supplements al Nuovo Cim., I:3 (1963), 859–1033 | DOI | MR

[5] Petrina D. Ja., On summation of the contributions from the Feynman diagrams an existence theorem. I, II, III, preprinty, Naukova dumka, Kiev, 1967 | Zbl

[6] Schwinger J., “Euclidean quantum electrodynamic”, Phys. Rev., 115:3 (1959), 721–731 | DOI | MR | Zbl

[7] Symanzik K., “Euclidean quantum field theory. I. Equations for a scalar model”, J. Math. Ph., 7:3 (1966), 510–525 | DOI | MR

[8] Symanzik K., “The asymptotic condition and dispersion relations”, Lectures on field theory and the many-body problem, Academic Press, New York, 1961, 67–96 | MR

[9] Riss F., Sekefalvi-Nad, Lektsii po funktsionalnomu analizu, IL, M., 1954

[10] Berezin F. A., Metod vtorichnogo kvantovaniya, Nauka, M., 1965 | MR

[11] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR