Renormalized asymptotic enumeration of Feynman diagrams

摘要

AbstractA 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. 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.Highlights?Asymptotic results for the perturbative expansions inD=0QFT are provided.?The method can be used to enumerate various graph classes asymptotically.?Full asymptotic expansions in different theories are given as examples.]]>