CONNECTION BETWEEN THE RENORMALIZATION GROUPS OF STÜCKELBERG–PETERMANN AND WILSON

Abstract

The Stückelberg–Petermann renormalization group is the group of finite renormalizations of the S-matrix in the framework of causal perturbation theory. The renormalization group in the sense of Wilson relies usually on a functional integral formalism, it describes the dependence of the theory on a UV-cutoff Λ; a widespread procedure is to construct the theory by solving Polchinski's flow equation for the effective potential.To clarify the connection between these different approaches we proceed as follows: in the framework of causal perturbation theory we introduce an UV-cutoff Λ, define an effective potential VΛ, prove a pertinent flow equation and compare with the corresponding terms in the functional integral formalism. The flow of VΛ is a version of Wilson's renormalization group. The restriction of these operators to local interactions can be approximated by a subfamily of the Stückelberg–Petermann renormalization group.