DOI 10.1007/s100529900234
On the trees of quantum fields
Ch. Brouder
Laboratoire de Minéralogie-Cristallographie, CNRS
UMR7590, Universités Paris 6, Paris 7, IPGP, Case 115, 4 place
Jussieu, 75252 Paris Cedex 05, France (e-mail:
brouder@lmcp.jussieu.fr)
Received: 6 July 1999 / Published online: 10 December 1999
Abstract
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
