Noncommutative renormalization for massless QED

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dc.creatorBrouder, Christian
dc.creatorFrabetti, Alessandra
dc.date2000-11-17
dc.date2000-11-21
dc.date.accessioned2026-07-07T04:10:56Z
dc.date.available2026-07-07T04:10:56Z
dc.descriptionWe study the renormalization of massless QED from the point of view of the Hopf algebra discovered by D. Kreimer. For QED, we describe a Hopf algebra of renormalization which is neither commutative nor cocommutative. We obtain explicit renormalization formulas for the electron and photon propagators, for the vacuum polarization and the electron self-energy, which are equivalent to Zimmermann's forest formula for the sum of all Feynman diagrams at a given order of interaction. Then we extend to QED the Connes-Kreimer map defined by the coupling constant of the theory (i.e. the homomorphism between some formal diffeomorphisms and the Hopf algebra of renormalization) by defining a noncommutative Hopf algebra of diffeomorphisms, and then showing that the renormalization of the electric charge defines a homomorphism between this Hopf algebra and the Hopf algebra of renormalization of QED. Finally we show that Dyson's formulas for the renormalization of the electron and photon propagators can be given in a noncommutative (e.g. matrix-valued) form.
dc.description50 pages, use feynmf package. Abstract and typos corrected
dc.identifierhttps://arxiv.org/abs/hep-th/0011161
dc.identifierhttp://arxiv.org/abs/hep-th/0011161
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/50387
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleNoncommutative renormalization for massless QED
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