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Quantum field theory meets Hopf algebra
Author(s) -
Brouder Christian
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610828
Subject(s) - hopf algebra , mathematics , noncommutative geometry , representation theory of hopf algebras , quasitriangular hopf algebra , feynman diagram , quantum group , quantum field theory , algebra over a field , renormalization , pure mathematics , division algebra , field (mathematics) , algebraic number , current algebra , mathematical physics , mathematical analysis
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)