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arXiv · hep-ph/0211188

Unique factorization in perturbative QFT

D. Kreimer
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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.

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D. Kreimer. 2002-11-13. Unique factorization in perturbative QFT. https://doi.org/10.1016/s0920-5632(03)80206-2

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