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 TMF, 2000, Volume 123, Number 3, Pages 452–461 (Mi tmf615)

Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory

V. V. Belokurova, Yu. P. Solov'evb, E. T. Shavgulidzeb

a M. V. Lomonosov Moscow State University, Faculty of Physics
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new high-accuracy method is suggested for calculating physical quantities for which only finitely many terms of the divergent series in a traditional perturbation theory are known. The method is based on approximating the desired quantity with the sum of finitely many terms of an absolutely convergent series. As an example, the $\beta$-function in the $\varphi_4^4$ model and the critical exponent $\alpha$ characterizing the behavior of the $\mathrm{He}^4$ heat capacity near the phase transition point are calculated.

DOI: https://doi.org/10.4213/tmf615

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English version:
Theoretical and Mathematical Physics, 2000, 123:3, 792–800

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Revised: 21.01.2000

Citation: V. V. Belokurov, Yu. P. Solov'ev, E. T. Shavgulidze, “Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory”, TMF, 123:3 (2000), 452–461; Theoret. and Math. Phys., 123:3 (2000), 792–800

Citation in format AMSBIB
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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. 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
2. V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. Shavgulidze, “Yurii Petrovich Solov'ev (obituary)”, Russian Math. Surveys, 59:5 (2004), 941–947
3. Efimov, GV, “Blokhintsev and nonlocal quantum field theory”, Physics of Particles and Nuclei, 35:5 (2004), 598
4. V. V. Belokurov, E. T. Shavgulidze, “Nelineinye nelokalnye zameny peremennykh v funktsionalnykh integralakh”, Fundament. i prikl. matem., 21:5 (2016), 47–59
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