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 TMF, 1983, Volume 57, Number 3, Pages 363–372 (Mi tmf2268)

Corrections to the asymptotic expressions for the higher orders of perturbation theory

Yu. A. Kubyshin

Abstract: A technique is developed for calculating the corrections in $1/n$ to the asymptotic expression for the $n$-th term of the perturbation series for the example of the scalar massless model $\varphi_{(4)}^4$ with internal symmetry $O(N)$. The first correction for the $\beta$ function is obtained.

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English version:
Theoretical and Mathematical Physics, 1983, 57:3, 1196–1202

Bibliographic databases:

Citation: Yu. A. Kubyshin, “Corrections to the asymptotic expressions for the higher orders of perturbation theory”, TMF, 57:3 (1983), 363–372; Theoret. and Math. Phys., 57:3 (1983), 1196–1202

Citation in format AMSBIB
\Bibitem{Kub83} \by Yu.~A.~Kubyshin \paper Corrections to the asymptotic expressions for the higher orders of perturbation theory \jour TMF \yr 1983 \vol 57 \issue 3 \pages 363--372 \mathnet{http://mi.mathnet.ru/tmf2268} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=735395} \transl \jour Theoret. and Math. Phys. \yr 1983 \vol 57 \issue 3 \pages 1196--1202 \crossref{https://doi.org/10.1007/BF01018746} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983SY87100004} 

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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. Yu. A. Kubyshin, “Sommerfeld–Watson summation of perturbation series”, Theoret. and Math. Phys., 58:1 (1984), 91–97
2. I. D. Mandzhavidze, A. N. Sisakyan, “Perturbation theory in the neighborhood of extended objects”, Theoret. and Math. Phys., 123:3 (2000), 776–791
3. M. V. Komarova, M. Yu. Nalimov, “Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the $(4?\epsilon)$-Dimensionally Regularized $O(n)$-Symmetric $\phi^4$ Theory”, Theoret. and Math. Phys., 126:3 (2001), 339–353
4. Yudin, IL, “Perturbation theory with convergent series: the calculation of the lambda phi(4)((4))-field theory beta-function”, Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment, 502:2–3 (2003), 633
5. M. V. Komarova, M. Yu. Nalimov, “Large-order asymptotic terms in perturbation theory: The first $(4-\epsilon)$-expansion correction to renormalization constants in the $O(n)$-symmetric theory”, Theoret. and Math. Phys., 143:2 (2005), 664–680
6. Kompaniets M.V. Panzer E., “Minimally Subtracted Six-Loop Renormalization of O(N)-Symmetric Phi(4) Theory and Critical Exponents”, Phys. Rev. D, 96:3 (2017), 036016
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