Connection between the renormalization groups of Stückelberg-Petermann and Wilson

Michael Dütsch
December 27, 2010
The Stueckelberg-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 $\Lambda$; 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 $\Lambda$, define an effective potential $V_\Lambda$, prove a pertinent flow equation and compare with the corresponding terms in the functional integral formalism. The flow of $V_\Lambda$ is a version of Wilson's renormalization group. The restriction of these operators to local interactions can be approximated by a subfamily of the Stueckelberg-Petermann renormalization group.
open access link Confluentes Mathematici, Vol. 4, No. 1 (2012) 12400014
@article{Duetsch:2010ab, author = "Duetsch, Michael", title = "{Connection between the Renormalization Groups of St\'uckelberg-Petermann and Wilson}", year = "2010", eprint = "1012.5604", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = ARXIV:1012.5604;%%" }