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.
@article{CML_2012__4_1_A2_0,
author = {Michael D\"utsch},
title = {Connection between the renormalization groups of {St\"uckelberg{\textendash}Petermann} and {Wilson}},
journal = {Confluentes Mathematici},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {4},
number = {1},
year = {2012},
doi = {10.1142/S1793744212400014},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744212400014/}
}
TY - JOUR AU - Michael Dütsch TI - Connection between the renormalization groups of Stückelberg–Petermann and Wilson JO - Confluentes Mathematici PY - 2012 VL - 4 IS - 1 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744212400014/ DO - 10.1142/S1793744212400014 LA - en ID - CML_2012__4_1_A2_0 ER -
%0 Journal Article %A Michael Dütsch %T Connection between the renormalization groups of Stückelberg–Petermann and Wilson %J Confluentes Mathematici %D 2012 %V 4 %N 1 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744212400014/ %R 10.1142/S1793744212400014 %G en %F CML_2012__4_1_A2_0
Michael Dütsch. Connection between the renormalization groups of Stückelberg–Petermann and Wilson. Confluentes Mathematici, Tome 4 (2012) no. 1. doi : 10.1142/S1793744212400014. https://cml.centre-mersenne.org/articles/10.1142/S1793744212400014/
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