Geodesic
On differential equations for the Feynman integral of a one-loop diagram
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 380-387 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Feynman integral $I(s,t)$ for one-loop diagram with four vertices is considered. With the aid of the Griffiths' method of differentiating rational differential forms with respect to the parameter, it is proved that $I(s,t)$ satisfies the system of two first order differential equations. From this system a hyperbolic partial differential equation for $I(s,t)$ is obtained, the main coefiicient of which vanishes on the Landau's manifold of the Feynman integral. 
@article{TMF_1971_9_3_a7,
     author = {V. A. Golubeva},
     title = {On differential equations for the {Feynman} integral of a~one-loop diagram},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {380--387},
     year = {1971},
     volume = {9},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a7/}
}
TY  - JOUR
AU  - V. A. Golubeva
TI  - On differential equations for the Feynman integral of a one-loop diagram
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 380
EP  - 387
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a7/
LA  - ru
ID  - TMF_1971_9_3_a7
ER  - 
%0 Journal Article
%A V. A. Golubeva
%T On differential equations for the Feynman integral of a one-loop diagram
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 380-387
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a7/
%G ru
%F TMF_1971_9_3_a7
V. A. Golubeva. On differential equations for the Feynman integral of a one-loop diagram. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 380-387. http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a7/

[1] G. Ponzano, T. Regge, “The monodromy group of one-loop relativistic Feinman integrals”, Problemy teoreticheskoi fiziki, Sb., «Nauka», 1969

[2] Zh. Lere, Differentsialnoe i integralnoe ischislenie na kompleksnom analiticheskom mnogoobrazii, IL, 1961 | MR

[3] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, v. 1, Fizmatgiz, 1958 | MR

[4] D. Fotiady, M. Froissart, J. Lascoux, F. Pham, Topology, 4 (1965), 159 | DOI | MR

[5] D. Fotiady, F. Pham, “Analytic study of some Feynman graphs by homological method”, V kn.: R. Hwa, V. Teplitz, Homologie and Feynman Integrals, Appendix VI, Benjamin, 1966 | MR

[6] J. B. Boyling, J. Math. Phys., 7 (1966), 1050 | DOI | MR

[7] J. Tarski, J. Math. Phys., 1 (1960), 429 | DOI | MR

[8] V. V. Golubev, Lektsii po analiticheskoi teorii differentsialnykh uravnenii, GITTL, 1950 | MR

[9] A. Krattser, K. Frants, Transtsendentnye funktsii, IL, 1963

[10] R. J. Eden, P. V. Landshoff, D. J. Olive, J. C. Polkinghorne, The Analytic $S$-Matrix, Cambridge University Press, 1966 | MR | Zbl

[11] T. Regge, G. Barucchi, Nuovo Cim., 34 (1964), 106 | DOI | MR

[12] E. Gursa, Kurs matematicheskogo analiza, t. III, ch. 1, GTTI, 1933 | MR

[13] P. Appell, J. Kampé de Fériet, Fonctions Hypergeometriques et Hyperspheriques, Gauthier-Villars, 1926

[14] G. Ponzano, T. Regge, E. G. Speer, M. J. Westwater, Comm. Math. Phys., 15 (1969), 83 | DOI | MR | Zbl

[15] P. A. Griffiths, Ann. Math., Ser. 2, 90 (1969), 460 | DOI | MR | Zbl