Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series
Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 3, pp. 302-310
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It is shown within the framework of nonlocal quantum theory of a one-component scalar field
go that for significantly nonlinear interaction Lagrangians $L_I(x)=gU(\varphi(x))$ such that the function $U(\alpha)$ satisfies the condition
$$
\lim_{\alpha\to\pm\infty}\vert U(\alpha)\vert=0,
$$
it is possible to choose the noniocal formfactor in such a manner that the $S$-matrix will be finite and unitary in every order of perturbation theory and the perturbation-theory series will converge absolutely in a Euclidean domain.
@article{TMF_1970_2_3_a3,
author = {G. V. Efimov},
title = {Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {302--310},
publisher = {mathdoc},
volume = {2},
number = {3},
year = {1970},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a3/}
}
TY - JOUR AU - G. V. Efimov TI - Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1970 SP - 302 EP - 310 VL - 2 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a3/ LA - ru ID - TMF_1970_2_3_a3 ER -
%0 Journal Article %A G. V. Efimov %T Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series %J Teoretičeskaâ i matematičeskaâ fizika %D 1970 %P 302-310 %V 2 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a3/ %G ru %F TMF_1970_2_3_a3
G. V. Efimov. Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series. Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 3, pp. 302-310. http://geodesic.mathdoc.fr/item/TMF_1970_2_3_a3/