Geodesic
Convergence of the perturbation series for a nonlocal nonpolynomial theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 281-290 Cet article a éte moissonné depuis la source Math-Net.Ru

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In [2,3] the perturbation series in the translationally invariant case is shown to converge on the basis of correspondence with statistical theory. In the present paper, a direct estimate is made for the logarithm of the generating functional of the Euclidean $s$ matrix and an upper bound for the radius of convergence with respect to the coupling constant is obtained; this is proportional to $m^2/\Lambda$, where $m$ is the mass of the particle and $\Lambda$ is the small coupling constant. 
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     author = {A. G. Basuev},
     title = {Convergence of the perturbation series for a nonlocal nonpolynomial theory},
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A. G. Basuev. Convergence of the perturbation series for a nonlocal nonpolynomial theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 281-290. http://geodesic.mathdoc.fr/item/TMF_1973_16_3_a0/

[1] G. V. Efimov, Preprint P2-4546, OIYaI, 1969 | MR

[2] D. Ya. Petrina, V. I. Skripnik, TMF, 8 (1971), 369

[3] D. Fivel, Phys. Rev., D4 (1971), 1653

[4] G. V. Efimov, Preprint ITF-68-52, Kiev, 1968

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

[6] R. P. Feynman, Rev. Mod. Phys., 20 (1947), 376 | MR

[7] K. Symanzik, Rendikonti della Scuolla Internasinalle di Fisica “Enrico Fermi” (Varenna, 1968), Acad. Press, 1969