Asymptotic Estimate of Perturbation Theory at Large Orders

  • Jean Zinn-Justin
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 39)


In these lectures we want to show how a new method, due to Lipatov, and based on a steepest descent evaluation of the euclidean path integral, allows one to estimate the coefficients of the perturbative expansion at large orders. For boson field theories one finds in general that the Kth order of perturbation theory behaves like:
$$K!{a^K}\,\,{K^b}\,\,c\,\,\left( {\,1\,\, + \,\,0\,\,\left( {\frac{1}{k}} \right)\,\,} \right)$$
where a depends only on the interaction, where b and c depend on the particular Green’s function one is calculating.


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© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Jean Zinn-Justin
    • 1
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA

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