Geodesic
Renormalization functional relationships in quantum electrodynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 2, pp. 219-234 Cet article a éte moissonné depuis la source Math-Net.Ru

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Gell-Mann–Low type asymptotic functional relationships for Green's functions are deduced for the electron mass renormalization $\delta m=mF(\Lambda/m, \alpha)$ and the photon and electron wave function renormalization constants $Z_3(\Lambda/m,\alpha)$ and $Z_2(\Lambda/m,\alpha)$, respectively. These are regarded as functions of the cutoff parameter $\Lambda$, the renormalized mass $m$, and the renormalized coupling constant $\alpha$. The relationships obtained are used to investigate the following problems: the existence of a solution of the “superconducting type” for the self-energy of the electron; the nature of the divergences in quantum electrodynamics; and the self-consistency of the theory. An approximation scheme is developed in order to determine the above functions; it is based on the functional relationships obtained and perturbation theory. 
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     title = {Renormalization functional relationships in quantum electrodynamics},
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V. I. Truten'; P. I. Fomin. Renormalization functional relationships in quantum electrodynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 2, pp. 219-234. http://geodesic.mathdoc.fr/item/TMF_1970_5_2_a4/

[1] Y. Nambu, Phys. Rev. Lett., 4 (1960), 380 ; Y. Nambu, G. Jona-Lasinio, Phys. Rev., 122 (1961), 345 | DOI | DOI | MR

[2] V. G. Vaks, A. I. Larkin, ZhETF, 40 (1961), 282 | Zbl

[3] P. I. Fomin, Pisma ZhETF, 6 (1967), 972; П. И. Фомин, В. И. Трутень, ЯФ, 9 (1969), 838

[4] P. I. Fomin, II Mezhdunarodnoe soveschanie po nelokalnoi kvantovoi teorii polya, Azau, 1970 (to appear)

[5] G. Källen, Dan. Mat. Fys. Medd., 27:12 (1953) ; K. Johnson, M. Baker, R. Willey, Phys. Rev., 136B (1964), 1111 ; 163 (1967), 1699 ; ЖЭТФ, 52 (1967), 318 | MR | Zbl | DOI | MR | DOI

[6] L. D. Landau, I. Ya. Pomeranchuk, DAN SSSR, 102 (1955), 489 | Zbl

[7] P. Redmond, Phys. Rev., 112 (1958), 1404 ; Н. Н. Боголюбов, А. А. Логунов, Д. В. Ширков, ЖЭТФ, 37 (1959), 805 ; Б. Л. Воронов, ЖЭТФ, 54 (1968), 1816 | DOI | MR | Zbl | Zbl

[8] M. Gell-Mann, F. Low, Phys. Rev., 95 (1954), 1300 | DOI | MR | Zbl

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

[10] P. I. Fomin, ZhETF, 43 (1962), 1934

[11] A. I. Akhiezer, V. B. Berestetskii, Kvantovaya elektrodinamika, II izd., Fizmatgiz, 1959 | MR

[12] D. Yennie, S. Frautschi, H. Suura, Ann. Phys., 13 (1961), 379 | DOI

[13] H. Lehmann, Nuovo Cim., 11 (1954), 342 | DOI | MR | Zbl

[14] L. D. Landau, A. A. Abrikosov, I. M. Khalatnikov, DAN SSSR, 95, 497 ; 773 ; (1954), 1177 ; 96 (1954), 261 | Zbl | Zbl | Zbl | Zbl

[15] R. Jost, J. Luttinger, Helv. Phys. Acta, 23 (1950), 201 | MR | Zbl

[16] V. I. Truten, P. I. Fomin, ZhETF, 57 (1969), 1280

[17] P. I. Fomin, V. I. Truten, ZhETF, 59 (1970), 890