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Numerical analysis of convergent perturbation expansions in quantum theory

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Abstract

We present the results of a numerical analysis of the convergence of the new perturbation expansion recently proposed by Belokurov, Solovyev, and Shavgulidze. Two particular examples are considered: the anharmonic oscillator in quantum mechanics and the renormalization group β-function in field theory. It is shown that in the first case, the series converges to an exact value in a wide range of expansion parameters. This range can be enlarged with the help of the Padé approximation. In field theory, the results have a stronger dependence on the regularization parameter. We discuss an algorithm for choosing this parameter that produces stable results.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, Russia

    D. I. Kazakov

  2. Moscow Physicotechnical Institute, USSR

    A. I. Onitchenko

Authors
  1. D. I. Kazakov
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  2. A. I. Onitchenko
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Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 291–297, February, 1997.

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Kazakov, D.I., Onitchenko, A.I. Numerical analysis of convergent perturbation expansions in quantum theory. Theor Math Phys 110, 229–234 (1997). https://doi.org/10.1007/BF02630448

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  • DOI: https://doi.org/10.1007/BF02630448

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