TY - JOUR
AB - 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.
AU - Kajantie, K.,
AU - Laine, Mikko
AU - Schroeder, York
ID - 1963777
IS - 4
JF - Phys.Rev. D
KW - n-point function
KW - perturbation theory
KW - 11.15.Bt
KW - 11.10.Wx
KW - 12.38.Bx
KW - Dyson-Schwinger equation
KW - fermion
KW - Feynman graph
KW - gauge field theory: SU(N)
KW - Phenomenology-HEP
KW - phi**n model
SN - 0556-2821
TI - A Simple way to generate high order vacuum graphs
VL - 65
ER -