Renormalization as a functor on bialgebras

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dc.creatorBrouder, Christian
dc.creatorSchmitt, William
dc.date2002-10-10
dc.date2007-04-10
dc.date.accessioned2026-07-07T10:34:15Z
dc.date.available2026-07-07T10:34:15Z
dc.descriptionThe Hopf algebra of renormalization in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalization endows T(T(B)^+), the double tensor algebra of B, with the structure of a noncommutative bialgebra. When the bialgebra B is commutative, renormalization turns S(S(B)^+), the double symmetric algebra of B, into a commutative bialgebra. The usual Hopf algebra of renormalization is recovered when the elements of B are not renormalised, i.e. when Feynman diagrams containing one single vertex are not renormalised. When B is the Hopf algebra of a commutative group, a homomorphism is established between the bialgebra S(S(B)^+) and the Faa di Bruno bialgebra of composition of series. The relation with the Connes-Moscovici Hopf algebra of diffeomorphisms is given. Finally, the bialgebra S(S(B)^+) is shown to give the same results as the standard renormalisation procedure for the scalar field.
dc.description24 pages, no figure. Several changes in the connection with standard renormalization
dc.identifierhttps://arxiv.org/abs/hep-th/0210097
dc.identifierhttp://arxiv.org/abs/hep-th/0210097
dc.identifierJ.Pure.Appl.Algebra209:477,2007
dc.identifierdoi:10.1016/j.jpaa.2006.06.013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/179412
dc.subjectHigh Energy Physics - Theory
dc.titleRenormalization as a functor on bialgebras
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