Eur. Phys. J. C 19, 715-741
DOI: 10.1007/s100520100586
Renormalization of QED with planar binary trees
Ch. Brouder1 and A. Frabetti21 Laboratoire de Minéralogie-Cristallographie, CNRS UMR7590, Universités Paris 6 et 7, IPGP, 4 place Jussieu, 75252 Paris Cedex 05, France
2 Institut de Recherche Mathématique Avancée, CNRS UMR 7501, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France
(Received: 23 March 2000 / Revised version: 24 November 2000 / Published online: 6 April 2001 -© Springer-Verlag 2001)
Abstract
The Dyson relations between
renormalized and bare photon and electron
propagators
and
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.
© Società Italiana di Fisica, Springer-Verlag 2001
