Theoretical and Mathematical Physics

, Volume 109, Issue 1, pp 1287–1293 | Cite as

Method of approximate evaluation of path integrals using perturbation theory with convergent series. I

  • V. V. Belokurov
  • Yu. P. Solov'ev
  • E. T. Shavgulidze


We propose a method of evaluating path integrals such that the integral is approximated with any accuracy by summations of a finite number of terms of an absolutely convergent series.


Perturbation Theory Finite Number Path Integral Convergent Series Approximate Evaluation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. N. Bogoliubov and D. V. Shirkov,Introduction to the Theory of Quantum Fields, Wiley, New York (1959).Google Scholar
  2. 2.
    J.-C. Le Guillou and J. Zinn-Justin (eds.),Large-Order Behaviour of Perturbation Theory, North-Holland, Amsterdam (1990).Google Scholar
  3. 3.
    D. I. Kazakov and D. V. Shirkov,Fortschr. Phys.,28, 465 (1980).Google Scholar
  4. 4.
    V. V. Kozlov,Symmetries, Topology, and the Resonances in Hamiltonian Mechanics [in Russian], Udmurtian State University, Izhevsk (1995).Google Scholar
  5. 5.
    R. B. Dingle,Asymptotic Expansions: Their Derivation and Interpretation, Academic Press, London-New York (1973).Google Scholar
  6. 6.
    I. S. Gradshtein and I. M. Ryzhik,Tables of Integrals, Series, and Products, Academic Press, New York (1980).Google Scholar
  7. 7.
    A. N. Kolmogorov and S. V. Fomin,Elements de la Theorie des Fonctions et de l'Analyse Fonctionelle, Ellipsis, Paris (1994).Google Scholar
  8. 8.
    O. G. Smolianov and E. T. Shavgulidze,Path Integrals, Izd. Mosk. Univ., Moscow (1990).Google Scholar
  9. 9.
    D. I. Kazakov and A. I. Onishchenko,Teor. Mat. Fiz.,110, No. 2, 291–297.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. V. Belokurov
    • 1
  • Yu. P. Solov'ev
    • 1
  • E. T. Shavgulidze
    • 1
  1. 1.Moscow State UniversityUSSR

Personalised recommendations