Renormalized asymptotic enumeration of Feynman diagrams

Michael Borinsky

doi:10.1016/j.aop.2017.07.009

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arXiv · 1703.00840

Renormalized asymptotic enumeration of Feynman diagrams

Michael Borinsky

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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.

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Michael Borinsky. 2017-03-02. Renormalized asymptotic enumeration of Feynman diagrams. https://doi.org/10.1016/j.aop.2017.07.009

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