A Simple way to generate high order vacuum graphs
Kajantie, K.,
Laine, Mikko
Schroeder, York
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
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.
2002
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/1963777
Kajantie K,, Laine M, Schroeder Y. A Simple way to generate high order vacuum graphs. <em>Phys.Rev. D</em>. 2002;65(4):045008.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.65.045008
info:eu-repo/semantics/altIdentifier/issn/0556-2821
info:eu-repo/semantics/altIdentifier/issn/1089-4918
info:eu-repo/semantics/altIdentifier/wos/000174043800067
info:eu-repo/semantics/altIdentifier/arxiv/hep-ph/0109100
info:eu-repo/semantics/closedAccess