A Geometrical Formulation of the Renormalization Group Method for Global Analysis
Teiji Kunihiro
TL;DR
This paper presents a geometrical formulation of the renormalization group method for global analysis, clarifying its effectiveness and providing a deeper understanding of its mathematical foundation.
Contribution
It introduces a geometrical approach based on envelope theory to the RG method, enhancing its theoretical basis and explaining its improvements.
Findings
The RG equation enhances the accuracy of global analysis.
The geometrical formulation clarifies the mathematical basis of the RG method.
The approach provides a unified framework for understanding RG improvements.
Abstract
On the basis of the classical theory of envelopes, we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.
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