Geodesic
On the $\alpha$-representation of Feynman integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 3, pp. 356-365 
B. M. Stepanov. On the $\alpha$-representation of Feynman integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 3, pp. 356-365. http://geodesic.mathdoc.fr/item/TMF_1970_5_3_a3/
@article{TMF_1970_5_3_a3,
     author = {B. M. Stepanov},
     title = {On the $\alpha$-representation of {Feynman} integrals},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {356--365},
     year = {1970},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_5_3_a3/}
}
TY  - JOUR
AU  - B. M. Stepanov
TI  - On the $\alpha$-representation of Feynman integrals
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1970
SP  - 356
EP  - 365
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1970_5_3_a3/
LA  - ru
ID  - TMF_1970_5_3_a3
ER  - 
%0 Journal Article
%A B. M. Stepanov
%T On the $\alpha$-representation of Feynman integrals
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1970
%P 356-365
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1970_5_3_a3/
%G ru
%F TMF_1970_5_3_a3

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

Graph theory is used to prove a formula for the integral over the internal momenta in the $\alpha$-representation of a Feynman integral. The distinctive feature of this formula is its explicit symmetry with respect to the choice of a tree in the graph.

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

[2] N. N. Bogoliubow, O. S. Parasiuk, Acta Math., 97 (1957), 227 | DOI | MR | Zbl

[3] V. S. Vladimirov, A. A. Logunov, Izv. AN SSSR, ser. matem., 23 (1959), 661 | MR | Zbl

[4] A. V. Astakhov, O. I. Zavyalov, A. D. Sukhanov, ZhETF, 52 (1967), 780

[5] J. S. R. Chisholm, Proc. Cambr. Phil. Soc., 48 (1952), 300 | DOI | MR | Zbl

[6] N. Nakanishi, Prog. Theor. Phys., 17 (1957), 401 | DOI | MR | Zbl

[7] A. V. Efremov, Preprint R-1242, OIYaI, 1963

[8] K. Berzh, Teoriya grafov i ee primeneniya, IL, 1962