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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 110, Number 2, Pages 291–297
DOI: https://doi.org/10.4213/tmf968 (Mi tmf968) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Numerical analysis of convergent perturbation theory in quantum field theory

D. I. Kazakova, A. I. Onitchenkob

a Joint Institute for Nuclear Research
b Moscow Institute of Physics and Technology
Full-text PDF (220 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf968
Abstract: Results of numerical analysis of convergency for a new series of perturbation theory are presented. Two examples are considered: anharmonic oscillator in quantum mechanics and the renormalization group $\beta$-function in field theory. It is shown that in the former case the series converges to an exact value in the wide region of the expansion parameter. This region can be enlarged by using the Padé approximation. In the field theory case the results have the stronger dependence on the expansion parameter. An algorithm of choosing this parameter in such a way as to obtain stable results is discussed.
Received: 05.08.1996
English version:
Theoretical and Mathematical Physics, 1997, Volume 110, Issue 2, Pages 229–234
DOI: https://doi.org/10.1007/BF02630448
Bibliographic databases:
Language: Russian
Citation: D. I. Kazakov, A. I. Onitchenko, “Numerical analysis of convergent perturbation theory in quantum field theory”, TMF, 110:2 (1997), 291–297; Theoret. and Math. Phys., 110:2 (1997), 229–234
Citation in format AMSBIB
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\by D.~I.~Kazakov, A.~I.~Onitchenko
\paper Numerical analysis of convergent perturbation theory in quantum field theory
\jour TMF
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\pages 291--297
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\crossref{https://doi.org/10.4213/tmf968}
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\transl
\jour Theoret. and Math. Phys.
\yr 1997
\vol 110
\issue 2
\pages 229--234
\crossref{https://doi.org/10.1007/BF02630448}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XR12900008}
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  • https://doi.org/10.4213/tmf968
  • https://www.mathnet.ru/eng/tmf/v110/i2/p291
    • This publication is cited in the following 3 articles:
    1. Groote S. Koerner J.G. Pivovarov A.A., “Understanding Pt Results for Decays of Tau-Leptons Into Hadrons”, Phys. Part. Nuclei, 44:2 (2013), 285–298  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    2. Kazakov, DI, “On the summation of divergent perturbation series in quantum mechanics and field theory”, Journal of Experimental and Theoretical Physics, 95:4 (2002), 581  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    3. V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Method of approximate calculating path integrals by using perturbation theory with convergent series. I”, Theoret. and Math. Phys., 109:1 (1996), 1287–1293  mathnet  mathnet  crossref  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:108
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