Functional self-similarity and renormalization group symmetry in mathematical physics
Vladimir F. Kovalev, Dmitrij V. Shirkov
TL;DR
This paper reviews the development of functional self-similarity and renormalization group symmetries in mathematical physics, highlighting an algorithm for identifying these symmetries via Lie group theory.
Contribution
It introduces a regular algorithm for discovering renormalization group symmetries using modern Lie group transformation theory.
Findings
Development of a regular algorithm for symmetry detection
Application of Lie groups to boundary-value problems
Enhanced understanding of renormalization group symmetries in physics
Abstract
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the regular algorithm for finding renormalization group-type symmetries using the contemporary theory of Lie groups of transformations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic and Geometric Analysis · advanced mathematical theories