Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries

Details Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries

1999-04-07

arxiv.org/abs/hep-th/9904044v2

Lett.Math.Phys. 48 (1999) 85-96

Physics

High Energy Physics

High Energy Physics - Theory

Survey paper, 12 pages, epsf for figures, dedicated to Mosh\'e Flato, minor corrections, to appear in Lett.Math.Phys.48

Scientific paper

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.

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