Connection between the renormalization groups of Stückelberg–Petermann and Wilson
Confluentes Mathematici, Volume 4 (2012) no. 1.

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.

Published online:
DOI: 10.1142/S1793744212400014
Michael Dütsch 1

1
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Michael Dütsch. Connection between the renormalization groups of Stückelberg–Petermann and Wilson. Confluentes Mathematici, Volume 4 (2012) no. 1. doi : 10.1142/S1793744212400014. https://cml.centre-mersenne.org/articles/10.1142/S1793744212400014/

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