  We propose a new formalism for quantum field theory which is neither based on
functional integrals, nor on Feynman graphs, but on marked trees. This
formalism is constructive, i.e. it computes correlation functions through
convergent rather than divergent expansions. It applies both to Fermionic and
Bosonic theories. It is compatible with the renormalization group, and it
allows to define non-perturbatively {\it differential} renormalization group
equations. It accommodates any general stable polynomial Lagrangian. It can
equally well treat noncommutative models or matrix models such as the
Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time
background from its central place in QFT, paving the way for a nonperturbative
definition of field theory in noninteger dimension.
