Feynman diagrams and polylogarithms: shuffles and pentagons

Abstract

We summarize the Hopf algebra structure on Feynman diagrams and emphasize the interest in further algebraic structures hidden in Feynman graphs.

6p, 6 epsf figures, Talk given at "Loops and Legs in QFT", Bastei, April 2000

References in corpus (6)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Renormalization in quantum field theory and the Riemann-Hilbert problem II: the $\beta$-function, diffeomorphisms and the renormalization group
• Problems of the Strategy of Regions
• Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummation
• Shuffling quantum field theory
• Renormalization in quantum field theory and the Riemann-Hilbert problem

Cited by in corpus (4)

• Combinatorics of (perturbative) quantum field theory
• Classical Propagation of Strings across a Big Crunch/Big Bang Singularity
• Connes-Kreimer-Epstein-Glaser Renormalization
• Operator approach to analytical evaluation of Feynman diagrams