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arXiv · hep-ph/0109100

A simple way to generate high order vacuum graphs

K. Kajantie·M. Laine·Y. Schroder
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Abstract

We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible ("skeleton") expansion. The regrouping leads to skeletons containing only free propagators, together with "ring diagrams" containing all the self-energy insertions. As a consequence, relatively few diagrams need to be drawn and integrations carried out at any single stage of the computation and, in low dimensions, overlapping ultraviolet/infrared subdivergences can be cleanly isolated. As an illustration we enumerate the graphs contributing to the 4-loop free energy in QCD, explicitly in a continuum and more compactly in a lattice regularization.

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K. Kajantie, M. Laine, Y. Schroder. 2001-11-21. A simple way to generate high order vacuum graphs. https://doi.org/10.1103/physrevd.65.045008

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