✦ LIBER ✦

Quantum field theory meets Hopf algebra

✍ Scribed by Christian Brouder

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 313 KB
Volume: 282
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200610828

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S ‐matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and leads to a correspondence between Feynman diagrams and semi‐standard Young tableaux. Reciprocally, these concepts are used as models to derive Hopf algebraic constructions such as a connected coregular action or a group structure on the linear maps from S (V) to V. In many cases, noncommutative analogues are derived (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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