Quantum field theory meets Hopf algebra

Details Quantum field theory meets Hopf algebra Quantum field theory meets Hopf algebra

2006-11-14

arxiv.org/abs/hep-th/0611153v3

Mathematische Nachrichten 282,12:1664-1690, 2009

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 4 figures. Slightly edited version of the published paper

Scientific paper

10.1002/mana.200610828

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 lead 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 most cases, noncommutative analogues are derived.

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