Hopf algebras, from basics to applications to renormalization
Dominique Manchon
TL;DR
This paper provides an accessible overview of Hopf algebras and their applications to renormalization, focusing on Connes and Kreimer's work, including Birkhoff decomposition and scattering formulas.
Contribution
It offers a comprehensive presentation of Hopf algebra concepts and their role in renormalization, connecting foundational theory to practical applications.
Findings
Explains Birkhoff decomposition in Hopf algebras
Details scattering-type formulas in graded cases
Links Hopf algebra theory to renormalization techniques
Abstract
An extended version of a series of lectures given at Bogota in december 2002. It consists in a presentation of some aspects of Connes' and Kreimer's work on renormalization in the context of general connected Hopf algebras, in particular Birkhoff decomposition and, in the graded case, the scattering-type formula.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Operator Algebra Research