# Renormalized asymptotic enumeration of Feynman diagrams

## TL;DR

This paper introduces a method for deriving all-order asymptotic formulas for counting various classes of Feynman diagrams in zero-dimensional quantum field theory, using singularity analysis and hyperelliptic curve representations.

## Contribution

It develops a novel approach combining singularity analysis and resurgence techniques to obtain asymptotic enumeration of Feynman diagrams, including primitive and skeleton diagrams.

## Key findings

- Derived full asymptotic expansions for diagram counts
- Applied method to various quantum field theories
- Connected diagram enumeration results obtained

## 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.