Dynkin operators, renormalization and the geometric $\beta$ function
Abstract
In this paper, I show a close connection between renormalization and a generalization of the Dynkin operator in terms of logarithmic derivations. The geometric $\beta$ function, which describes the dependence of a Quantum Field Theory on an energy scale defines is defined by a complete vector field on a Lie group $G$ defined by a QFT. It also defines a generalized Dynkin operator.
 Publication:

arXiv eprints
 Pub Date:
 November 2012
 arXiv:
 arXiv:1211.4466
 Bibcode:
 2012arXiv1211.4466A
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Dynamical Systems