Renormalization theory of Feynman amplitudes on configuration spaces

In a previous paper “Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces” (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This approach is aimed to serve for developing an algebraic algorithm for computing the Gell–Mann–Low renormalization group action. In the present work we introduce a modification of the theory of renormalization maps for the case of Minkowski space and we give the way how it is combined with the causal perturbation theory.