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.

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