Branching Equations of I and II Type and Their Connections with Finite Equations of Motion and the Callan-Symanzik Equation

Abstract

The aim of this paper is to recall, and present in the context of today’s quantum field theory, some results which we found in a sequel of past works. Most of them were obtained many years ago¹⁾; our main objective was at the time to discriminate, by using appropriate techniques, combinatoric from analytic problems. The first were brought into a naturally compact form by introducing some algorithms, which need not be mentioned here; the second were treated, at the beginning of our research, by defining “finite parts” of all quantities of interest, together with the formal properties which had to be satisfied by them in order that combinatorics could apply. Specific definitions were also given for the computation of finite part integrals, but no special emphasis was then placed on this aspect of the problem.