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Unique factorization in perturbative QFT

✍ Scribed by D. Kreimer

Book ID
104354873
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
372 KB
Volume
116
Category
Article
ISSN
0920-5632

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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Criteria for unique factorization in int
Criteria for unique factorization in integral domains
✍ D.D. Anderson; Scott T. Chapman; Franz Halter-Koch; Muhammad Zafrullah πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 861 KB

Let R be an integral domain. In this paper, we introduce a sequence of factorization properties which are weaker than the classical UFD criteria. We give several examples of atomic nonfactorial monoids which satisfy these conditions, but show for several classes of integral domains of arithmetical i