Renormalized asymptotic enumeration of Feynman diagrams

Abstract

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis and is related to resurgence. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

49 pages; version 2: corrected typos, updated references, added minor clarifications

References in corpus (3)

• Renormalization of gauge fields: A Hopf algebra approach
• Hedin's equations and enumeration of Feynman's diagrams
• Algebraic lattices in QFT renormalization

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