Abstract:
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 m2/Λ, where m is the mass of the particle and Λ is the small coupling constant.
Citation:
A. G. Basuev, “Convergence of the perturbation series for a nonlocal nonpolynomial theory
m2/Λ”, TMF, 16:3 (1973), 281–290; Theoret. and Math. Phys., 16:3 (1973), 835–842
\Bibitem{Bas73}
\by A.~G.~Basuev
\paper Convergence of the perturbation series for a nonlocal nonpolynomial theory
$m^2/\Lambda$
\jour TMF
\yr 1973
\vol 16
\issue 3
\pages 281--290
\mathnet{http://mi.mathnet.ru/tmf3762}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=468865}
\transl
\jour Theoret. and Math. Phys.
\yr 1973
\vol 16
\issue 3
\pages 835--842
\crossref{https://doi.org/10.1007/BF01042421}
Linking options:
https://www.mathnet.ru/eng/tmf3762
https://www.mathnet.ru/eng/tmf/v16/i3/p281
This publication is cited in the following 5 articles:
Nikita A. Ignatyuk, Stanislav L. Ogarkov, Daniel V. Skliannyi, “Nonlocal Fractional Quantum Field Theory and Converging Perturbation Series”, Symmetry, 15:10 (2023), 1823
Guskov V.A. Ivanov M.G. Ogarkov S.L., “A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory”, Phys. Part. Nuclei, 52:3 (2021), 420–437
Matthew Bernard, Vladislav A. Guskov, Mikhail G. Ivanov, Alexey E. Kalugin, Stanislav L. Ogarkov, “Nonlocal Scalar Quantum Field Theory—Functional Integration, Basis Functions Representation and Strong Coupling Expansion”, Particles, 2:3 (2019), 385
Ivan Chebotarev, Vladislav Guskov, Stanislav Ogarkov, Matthew Bernard, “S-Matrix of Nonlocal Scalar Quantum Field Theory in Basis Functions Representation”, Particles, 2:1 (2019), 103
A. G. Basuev, “Convergence of the perturbation series for the Yukawa interaction”, Theoret. and Math. Phys., 22:2 (1975), 142–148
Citation in format AMSBIB
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