  A cohomological analysis of the renormalization freedom is performed in the
Epstein-Glaser scheme on a flat Euclidean space. We study the deviation from
commutativity between the renormalization and the action of all linear partial
differential operators. It defines a Hochschild 1-cocycle and the
renormalization ambiguity corresponds to a nonlinear subset in the cohomology
class of this renormalization cocycle. We have shown that the related
cohomology spaces can be reduced to de Rham cohomologies of the so called
"(ordered) configuration spaces". We have also found cohomological differential
equations that exactly determine the renormalization cocycles up to the
renormalization freedom. This analysis is a first step towards a new approach
for computing renormalization group actions. It can be also naturally extended
to manifolds as well as to the case of causal perturbation theory.
