Unique factorization in perturbative QFT

Abstract

We discuss factorization of the Dyson--Schwinger equations using the Lie- and Hopf algebra of graphs. The structure of those equations allows to introduce a commutative associative product on 1PI graphs. In scalar field theories, this product vanishes if and only if one of the factors vanishes. Gauge theories are more subtle: integrality relates to gauge symmetries.

5pages, Talk given at "RadCor 2002 - Loops and Legs 2002", Kloster Banz, Germany, Sep 8-13, 2002

References in corpus (2)

• Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
• Insertion and Elimination: the doubly infinite Lie algebra of Feynman graphs

Cited by in corpus (2)

• The massless two-loop two-point function
• Recursion and growth estimates in renormalizable quantum field theory