Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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

Keywords

High Energy Physics - Theory, Mathematical Physics, Quantum Algebra

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/56018

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/hep-th/9904044
 http://arxiv.org/abs/hep-th/9904044
 Lett.Math.Phys. 48 (1999) 85-96

Collections

arXiv