  We consider the structure of renormalizable quantum field theories from the
viewpoint of their underlying Hopf algebra structure. We review how to use this
Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative
results for the short-distance singular sector of a renormalizable quantum
field theory. We focus on the short-distance behaviour and thus discuss
renormalized Green functions $G_R(\alpha,L)$ which depend on a single scale
$L=\ln q^2/\mu^2$.
