Geodesic
Convergence of the perturbation series for the Yukawa interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 2, pp. 203-212 
A. G. Basuev. Convergence of the perturbation series for the Yukawa interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 22 (1975) no. 2, pp. 203-212. http://geodesic.mathdoc.fr/item/TMF_1975_22_2_a4/
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     title = {Convergence of the perturbation series for the {Yukawa} interaction},
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     number = {2},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the perturbation theory series in translation-invariant case and with the removed cut-off of boson propagator for the euclidean Green functions; converges if $|g|^2/\bar m\lambda^2/96\bar\Delta(0)$. Here $\bar m$ is a certain quantity which remains finite when the fermion propagator regularization is removed, $\lambda^2$ is the boson mass and $\bar\Delta(0)$ is the value of the fermion propagator at the point $x=0$ of the $x$-space. By means of other methods the same problem was considered in the work [6] for the pseudo-euclidean and in the work [5] for the euclidean Green functions.

[1] E. R. Caianello, Nuovo Cim., 10 (1953), 1634 | DOI

[2] D. R. Yennie, S. Cartenhaus, Nuovo Cim., 9 (1958), 59 | DOI | MR

[3] D. Ryuell, Statisticheskaya fizika, «Mir», 1971

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

[5] S. S. Ivanov, A. L. Rebenko, TMF, 11 (1972), 190 | MR

[6] I. Ya. Arefeva, TMF, 14 (1973), 3 | MR

[7] B. Symon, Nuovo Cim., 59A (1969), 199 | DOI

[8] F. A. Berezin, Metod vtorichnogo kvantovaniya, «Mir», 1965 | MR

[9] A. G. Basuev, TMF, 16 (1973), 283 | MR

[10] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, t. 2, Nauka, 1966, str. 427