Department of Physics and Astronomy, Open University, UK
Until recently we
knew of only two types of all-orders
summations of Feynman
diagrams: ladders and chains. Dirk
Kreimer's Hopf
algebra
of rooted trees
organizes the iterated
subtraction of
subdivergences generated by all possible
nestings and chainings
of primitive divergences. It thus
offers the prospect
of more powerful summations of
perturbative quantum
field theory. As a step in that
direction, I describe
the analytical, combinatoric and
Hopf-algebraic
structure of a recent successful summation of
diagrams whose
divergence structure is described by
undecorated rooted
trees, generated by a single skeleton
term. The exact
results are compared with Pade-Borel
resummation..