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 TMF, 1970, Volume 2, Number 3, Pages 302–310 (Mi tmf4035)

Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series

G. V. Efimov

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1970, 2:3, 217–223

Citation: G. V. Efimov, “Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series”, TMF, 2:3 (1970), 302–310; Theoret. and Math. Phys., 2:3 (1970), 217–223

Citation in format AMSBIB
\Bibitem{Efi70} \by G.~V.~Efimov \paper Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series \jour TMF \yr 1970 \vol 2 \issue 3 \pages 302--310 \mathnet{http://mi.mathnet.ru/tmf4035} \transl \jour Theoret. and Math. Phys. \yr 1970 \vol 2 \issue 3 \pages 217--223 \crossref{https://doi.org/10.1007/BF01038039} 

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This publication is cited in the following articles:
1. D. Ya. Petrina, V. I. Skripnik, “Kirkwood–Salzburg equations for the coefficient functions of the $S$ matrix”, Theoret. and Math. Phys., 8:3 (1971), 896–904
2. M. A. Soloviev, “On the Fourier–Laplace transformation of generalized functions”, Theoret. and Math. Phys., 15:1 (1973), 317–328
3. G. D. Romanko, I. V. Khimich, “Fourier transformation of a class of hyperfunctions and formulation of the condition of local commutativity in the framework of localizable quantum field theory in terms of hyperfunctions”, Theoret. and Math. Phys., 23:2 (1975), 451–461
4. A. L. Rebenko, “Mathematical foundations of equilibrium classical statistical mechanics of charged particles”, Russian Math. Surveys, 43:3 (1988), 65–116
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