Hopf algebra of graphs and the RG equations

Details Hopf algebra of graphs and the RG equations Hopf algebra of graphs and the RG equations

2004-08-30

arxiv.org/abs/hep-th/0408230v1

Theor.Math.Phys. 143 (2005) 505-514; Teor.Mat.Fiz. 143 (2005) 22-32

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 2 figures, LaTeX

Scientific paper

We study the renormalization group equations following from the Hopf algebra of graphs. Vertex functions are treated as vectors in dual to the Hopf algebra space. The RG equations on such vertex functions are equivalent to RG equations on individual Feynman integrals. The solution to the RG equations may be represented as an exponent of the beta-function. We explicitly show that the exponent of the one-loop beta function enables one to find the coefficients in front of the leading logarithms for individual Feynman integrals. The same results are obtained in parquet approximation.

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