A Simple way to generate high order vacuum graphs

Kajantie K,, Laine M, Schroeder Y (2002)
Phys.Rev. D 65(4).

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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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Kajantie K,, Laine M, Schroeder Y. A Simple way to generate high order vacuum graphs. Phys.Rev. D. 2002;65(4).
Kajantie, K. ,, Laine, M., & Schroeder, Y. (2002). A Simple way to generate high order vacuum graphs. Phys.Rev. D, 65(4).
Kajantie, K. ,, Laine, M., and Schroeder, Y. (2002). A Simple way to generate high order vacuum graphs. Phys.Rev. D 65.
Kajantie, K.,, Laine, M., & Schroeder, Y., 2002. A Simple way to generate high order vacuum graphs. Phys.Rev. D, 65(4).
K., Kajantie, M. Laine, and Y. Schroeder, “A Simple way to generate high order vacuum graphs”, Phys.Rev. D, vol. 65, 2002.
Kajantie, K.,, Laine, M., Schroeder, Y.: A Simple way to generate high order vacuum graphs. Phys.Rev. D. 65, (2002).
Kajantie, K.,, Laine, Mikko, and Schroeder, York. “A Simple way to generate high order vacuum graphs”. Phys.Rev. D 65.4 (2002).
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