This article is cited in 5 papers

The Hopf graph algebra and renormalization group equations

D. V. Malyshev<sup>abc

a</sup> M. V. Lomonosov Moscow State University
^b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
^c Princeton University

Abstract: We study the renormalization group equations implied by the Hopf graph algebra. The vertex functions are regarded as vectors in the dual space of the Hopf algebra. The renormalization group equations for these vertex functions are equivalent to those for individual Feynman integrals. The solution of the renormalization group equations can be represented in the form of an exponential of the beta function. We clearly show that the exponential of the one-loop beta function allows finding the coefficients of the leading logarithms for individual Feynman integrals. The calculation results agree with those obtained in the parquet approximation.

Keywords: Hopf graph algebra, renormalization group, leading logarithms.

Received: 07.09.2004

DOI: 10.4213/tmf1801

 English version: Theoretical and Mathematical Physics, 2005, 143:1, 505–514

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