Renormalization of QED with planar binary trees

  • Ch. Brouder
  • A. Frabetti
Theoretical physics


The Dyson relations between renormalized and bare photon and electron propagators \(Z_3 \bar D(q)=D(q)\) and \(Z_2 \bar S(q)=S(q)\) are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure.


Electron Charge Binary Tree Feynman Diagram Recursive Relation Perturbative Expansion 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ch. Brouder
    • 1
  • A. Frabetti
    • 2
  1. 1.Laboratoire de Minéralogie–Cristallographie, CNRS UMR7590, Universités Paris 6 et 7, IPGP, 4 place Jussieu, 75252 Paris Cedex 05, France FR
  2. 2.Institut de Recherche Mathématique Avancée, CNRS UMR 7501, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France FR

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