Hopf algebra approach to Feynman diagram calculations
Kurusch Ebrahimi-Fard, Dirk Kreimer
TL;DR
This paper reviews the Hopf algebra framework underlying Feynman diagrams, highlighting its role in renormalization within perturbative quantum field theory and discussing recent advances and future research directions.
Contribution
It provides a comprehensive overview of the Hopf algebra approach to Feynman diagram calculations and summarizes recent developments in the field.
Findings
Clarified the Hopf algebra structure in Feynman diagram renormalization
Summarized recent progress in the mathematical understanding of quantum field theory
Outlined future research directions in the area
Abstract
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an emphasis on further directions of research.
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