Simple way to generate high order vacuum graphs
- 24 January 2002
- journal article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 65 (4)
- https://doi.org/10.1103/physrevd.65.045008
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 and infrared subdivergences can be cleanly isolated. As an illustration we enumerate the graphs contributing to the four-loop free energy in QCD, explicitly in a continuum and more compactly in a lattice regularization. DOI: http://dx.doi.org/10.1103/PhysRevD.65.045008 © 2002 The American Physical SocietyKeywords
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