@article{1963777,
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.},
author = {Kajantie, K., and Laine, Mikko and Schroeder, York},
issn = {1089-4918},
journal = {Phys.Rev. D},
keyword = {n-point function, perturbation theory, 11.15.Bt, 11.10.Wx, 12.38.Bx, Dyson-Schwinger equation, fermion, Feynman graph, gauge field theory: SU(N), Phenomenology-HEP, phi**n model},
number = {4},
pages = {045008},
title = {{A Simple way to generate high order vacuum graphs}},
doi = {10.1103/PhysRevD.65.045008},
volume = {65},
year = {2002},
}