Renormalization of massive Feynman amplitudes and homogeneity (based on a joint work with Raymond Stora)

We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.