Distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space

Abstract

A detailed study of the distributional zero-mass limit of renormalized Feynman amplitudes is given inMinkowski space. Elementary rules are set up to prove the existence of the distributional zero-mass limit. To carry out the analysis, we reduce, in the process, the underlying estimates to the ones in Euclidean space, which in turn sets up a formalism for the study in Minkowski space. A main technical point that is encountered in the study of the e→+0 limit, and the partial integrations arising in the distributional definition over the external momenta are done without spoiling the structure of the original amplitudes. The study is very general as it permits the vanishingly small masses to approach zero at different rates. All subtractions of renormalization are carried out directly in moment space (at the origin) with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram.