Large order expansion in perturbation theory

John C. Collins, Davison E. Soper

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


We investigate the large n behavior of the perturbation coefficients En for the ground state energy of the anharmonic oscillator, considered as a field theory in one space-time dimension. We combine the saddle point expansion for functional integrals introduced in this context by Lipatov with the dispersion relation (in coupling constant) used by Bender and Wu. The complete Feynman rules for the expansion in 1 n are worked out, and we compute the first two terms, which agree with those computed by Bender and Wu using the WKB approximation. One feature of our analysis is a deformation of the integration contour in function space as one analytically continues in the coupling.

Original languageEnglish (US)
Pages (from-to)209-234
Number of pages26
JournalAnnals of Physics
Issue number1
StatePublished - May 1978

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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