Some aspects of the planar perturbation series

J. Koplik, A. Neveu, S. Nussinov

Research output: Contribution to journalArticlepeer-review


We discuss several features of the class of planar Feynman diagrams in perturbation theory. We show that the number of planar n-loop diagrams grows exponentially in n in any field theory, and calculate the detailed asymptotic behavior for φ3 and φ4. We discuss the implications of this result for the convergence of the series and its relation to various semiclassical instabilities, with special reference to non-Abelian gauge theories. We also derive a functional integral equation for planar graphs.

Original languageEnglish
Pages (from-to)109-131
Number of pages23
JournalNuclear Physics, Section B
Issue number1
StatePublished - 16 May 1977
Externally publishedYes


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