Dynkin operators, renormalization and the geometric β function

2012/11/19 by Susama Agarwala, Agarwala, Susama
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #hep-th #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.1211.4466

arxiv created 2012/11/19 · arxiv updated 2012/11/20

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 β 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.

Related

• Dynkin operators and renormalization group actions in pQFT
• The beta function of gauge theories at two loops in differential renormalization
• The Renormalisation Group Equation As An Equation For Lie Transport Of Amplitudes
• Analytical and Geometric approches of non-perturbative Quantum Field Theories
• Higher-order β-functions in the Standard Model and beyond