Unique factorization in perturbative QFT

Details Unique factorization in perturbative QFT Unique factorization in perturbative QFT

2002-11-13

arxiv.org/abs/hep-ph/0211188v1

Nucl.Phys.Proc.Suppl. 116 (2003) 392-396

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/S0920-5632(03)80206-2

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.

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