1999/04/13 by A. Connes, D. Kreimer
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.QA
published as Lett.Math.Phys. 48 (1999) 85-96 · Survey paper, 12 pages, epsf for figures, dedicated to Moshé Flato, minor corrections, to appear in Lett.Math.Phys.48
arxiv created 1999/04/13 · arxiv updated 2009/11/30
We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned out to be the key to a conceptual understanding of the subtraction procedure. We shall then describe several occurences of this or closely related Hopf algebras in other mathematical domains, such as foliations, Runge Kutta methods, iterated integrals and multiple zeta values. We emphasize the unifying role which the Butcher group, discovered in the study of numerical integration of ordinary differential equations, plays in QFT.