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

This article is cited in 4 scientific papers (total in 4 papers)

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

Received: 30.06.1969

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref
    2. M. A. Soloviev, “On the Fourier–Laplace transformation of generalized functions”, Theoret. and Math. Phys., 15:1 (1973), 317–328  mathnet  crossref  mathscinet
    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  mathnet  crossref  mathscinet  zmath
    4. A. L. Rebenko, “Mathematical foundations of equilibrium classical statistical mechanics of charged particles”, Russian Math. Surveys, 43:3 (1988), 65–116  mathnet  crossref  mathscinet  adsnasa  isi
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