Simple parametric integral representations of the regular (finite) and singular parts of divergent Feynman amplitudes. I. General expressions
Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 3, pp. 355-365 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Simple expressions are obtained that describe the regular (finite) and singular parts of the divergent Feynman amplitudes of the lowest nontrivial orders of perturbation theory irrespective of the form of the matrix elements and the type of quantum-field models with polynomial and quasipolynomial interaction in $n$-dimensional space-time.
@article{TMF_1982_51_3_a5,
     author = {V. I. Kucheryavyi},
     title = {Simple parametric integral representations of the regular (finite) and singular parts of divergent {Feynman} amplitudes. {I.~General} expressions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--365},
     year = {1982},
     volume = {51},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a5/}
}
TY  - JOUR
AU  - V. I. Kucheryavyi
TI  - Simple parametric integral representations of the regular (finite) and singular parts of divergent Feynman amplitudes. I. General expressions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1982
SP  - 355
EP  - 365
VL  - 51
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a5/
LA  - ru
ID  - TMF_1982_51_3_a5
ER  - 
%0 Journal Article
%A V. I. Kucheryavyi
%T Simple parametric integral representations of the regular (finite) and singular parts of divergent Feynman amplitudes. I. General expressions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1982
%P 355-365
%V 51
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a5/
%G ru
%F TMF_1982_51_3_a5
V. I. Kucheryavyi. Simple parametric integral representations of the regular (finite) and singular parts of divergent Feynman amplitudes. I. General expressions. Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 3, pp. 355-365. http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a5/

[1] Bogolyubov N. N., Parasyuk O. S., Izv. AN SSSR, ser. matem., 20 (1956), 585 | MR | Zbl

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

[3] Parasyuk O. S., UMZh, 12 (1960), 287

[4] Scherbina V. A., Deponirovano v VINITI, No 38–64, 1964 | Zbl

[5] Zavyalov O. I., Stepanov B. M., YaF, 1 (1965), 922

[6] Hepp K., Commun. Math. Phys., 2 (1966), 301 | DOI | Zbl

[7] Van der Kolk C. M., De Kerf E. A., Physica, A80 (1975), 339 | Zbl

[8] Zavyalov O. I., Perenormirovannye diagrammy Feinmana, Nauka, M., 1979 | MR

[9] Appelquist T., Ann. of Phys., 54 (1969), 27 | DOI | MR

[10] Bergere M. C., Zuber J. B., Commun. Math. Phys., 35 (1974), 113 | DOI | MR

[11] Speer E., Generalized Feynman Amplitudes, Princeton University Press, 1969 | MR

[12] Speer E. R., “Dimensional and Analytical Renormalization”, Renormalization Theory, ed. G. Velo, Wightman A. S., D. Reidel Publishing Company, Dordrecht, Holland, 1976, 25–93 | DOI | MR

[13] Gerdt V. P., Tarasov O. V., Shirkov D. V., UFN, 130 (1980), 113 | DOI | MR

[14] Kucheryavyi V. I., TMF, 20 (1974), 29

[15] Kucheriavy V. I., Nucl. Phys., B127 (1977), 66 | DOI | MR

[16] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. II, Nauka, M., 1974 | MR

[17] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. I, Nauka, M., 1974 | MR

[18] Khammermesh M., Teoriya grupp i ee primenenie k fizicheskim problemam, Mir, M., 1966

[19] Anikin S. A., Polivanov M. K., TMF, 21 (1974), 175–182 | MR

[20] Zimmerman W., Ann. of Phys., 77 (1973), 536 | DOI | MR

[21] Zimmerman W., Ann. of Phys., 77 (1973), 570 | DOI | MR

[22] Zavialov O. I., Publ. RIMS, Kyoto University, Suppl., 12 (1977), 481 | DOI | MR | Zbl