Geodesic
On equations for the matrix elements of Euclidean quantum electrodynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 301-316 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Equations are obtained for the elements of the $S$ matrix of Euclidean quantum electrodynamics. The generating operator of these equations is investigated. On the basis of the analogy between the interaction Hamiltonian and the generating operator it is shown (under certain restrictions on the form factor) that the perturbation series converge for arbitrary values of the coupling constant. 
@article{TMF_1972_11_3_a3,
     author = {A. L. Rebenko},
     title = {On equations for the matrix elements of {Euclidean} quantum electrodynamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {301--316},
     year = {1972},
     volume = {11},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a3/}
}
TY  - JOUR
AU  - A. L. Rebenko
TI  - On equations for the matrix elements of Euclidean quantum electrodynamics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1972
SP  - 301
EP  - 316
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a3/
LA  - ru
ID  - TMF_1972_11_3_a3
ER  - 
%0 Journal Article
%A A. L. Rebenko
%T On equations for the matrix elements of Euclidean quantum electrodynamics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1972
%P 301-316
%V 11
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a3/
%G ru
%F TMF_1972_11_3_a3
A. L. Rebenko. On equations for the matrix elements of Euclidean quantum electrodynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 301-316. http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a3/

[1] S. Tomonaga, Progr. Theor. Phys., 1 (1946), 27 ; J. Schwinger, Phys. Rev., 74 (1948), 1439 ; 75 (1949), 651 ; 76 (1949), 790 ; R. P. Feynman, Phys. Rev., 76, 749 ; (1949), 769 ; J. Dyson, Phys. Rev., 75 (1949), 1736 ; Noveishee razvitie kvantovoi elektrodinamiki, IL, 1954 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | Zbl | DOI | MR | Zbl

[2] J. C. Ward, Proc. Phys. Soc., A64 (1951), 54 | DOI | MR | Zbl

[3] A. Salam, Phys. Rev., 84 (1951), 426 | DOI | MR | Zbl

[4] N. N. Bogolubov, O. S. Parasyuk, Acta Math., 97 (1957), 227 ; Н. Н. Боголюбов, О. С. Парасюк, Изв. АН СССР, сер. матем., 20 (1956), 585 | DOI | MR | MR | Zbl

[5] G. V. Efimov, “Nelokalnaya kvantovaya teoriya skalyarnogo polya”, Problemy fiziki elementarnykh chastits i atomnogo yadra, Sb., 1, no. 1, Atomizdat, 1970, 225

[6] T. D. Lee, G. C. Wick, Phys. Rev., D2 (1970), 1033 | MR | Zbl

[7] A. Jaffe, Commun. Math. Phys., 1 (1966), 127 ; C. A. Hurst, Proc. Roy. Soc., London, A214 (1952), 44 ; W. E. Thirring, Helv. Phys. Acta, 26 (1953), 33 | DOI | MR | DOI | MR | Zbl | MR | Zbl

[8] V. I. Ogievetskii, DAN SSSR, 109 (1956), 919 | Zbl

[9] B. L. Ioffe, DAN SSSR, 94 (1954), 437 | MR | Zbl

[10] J. Schwinger, Phys. Rev., 117 (1959), 721 | DOI | MR

[11] E. S. Fradkin, DAN SSSR, 98 (1954), 47 ; ЖЭТФ, 29 (1954), 751 ; Труды физического института им. Лебедева АН СССР, 29, 1965, 7 | MR | Zbl | MR | Zbl

[12] K. Symansik, J. Math. Phys., 7 (1966), 510 | DOI | MR

[13] D. Ya. Petrina, Izv. AN SSSR, seriya matem., 32 (1968), 1052 | MR | Zbl

[14] D. Ya. Petrina, A. L. Rebenko, Preprint ITP-68-59, Kiev, 1967 | MR

[15] E. R. Caianiello, Nuovo Cim., 10 (1953), 1634 ; 11 (1954), 493 | DOI | MR | Zbl | DOI | MR

[16] T. Carleman, Les fonctions quasi-analitiques, Paris, 1926

[17] S. S. Ivanov, Preprint ITF-70-27, Kiev, 1967; С. С. Иванов, Д. Я. Петрина, ДАН СССР, 188 (1968), 7761

[18] F. A. Berezin, Metod vtorichnogo kvantovaniya, «Nauka», 1965 | MR

[19] G. C. Wick, Phys. Rev., 96 (1954), 1124 | DOI | MR | Zbl

[20] L. L. Foldy, S. A. Wouthuysen, Phys. Rev., 78 (1950), 29 | DOI | Zbl

[21] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, «Naukova dumka», 1965 | MR

[22] A. L. Rebenko, Preprint ITF-71-37E, Kiev, 1967

[23] S. S. Ivanov, A. L. Rebenko, Preprint ITF-71-38E, Kiev, 1967