Convolutions of particle Green’s functions

Summary

The use of Feynman causal function in the perturbative treatment of theS-matrix made the computation of convolutions an easy and well-known procedure for free-particle propagators. But the convolution of its components, like theδ and principal values among themselves, is very rarely looked upon. In field theories with higher-order equations of motion some of these convolutions appear as the fundamental ingredients. A discussion of these convolutions is explicitly done in the simplest examples.