On the trees of quantum fields
Laboratoire de Minéralogie-Cristallographie, CNRS
UMR7590, Universités Paris 6, Paris 7, IPGP, Case 115, 4 place
Jussieu, 75252 Paris Cedex 05, France (e-mail:
Received: 6 July 1999 / Published online: 10 December 1999
The solution of some equations involving functional derivatives is written as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are investigated. Several examples are treated in the case of quantum electrodynamics: the complete fermion and photon propagators, the two-body Green function and the one-body Green function in the presence of an external source, the complete vacuum polarization, the electron self-energy and the irreducible vertex.
Copyright Springer-Verlag 2000