Hopf Algebras, Renormalization and Noncommutative Geometry
Alain Connes, Dirk Kreimer
TL;DR
This paper investigates the connection between Hopf algebras used in quantum field theory renormalization and those in noncommutative geometry's index theory for foliations, revealing deep mathematical links.
Contribution
It establishes a novel relationship between Hopf algebras in quantum field theory and noncommutative geometry, bridging two mathematical frameworks.
Findings
Identifies a correspondence between Hopf algebras in QFT and NCG.
Provides insights into the algebraic structures underlying renormalization and index theory.
Suggests new avenues for applying algebraic methods across physics and geometry.
Abstract
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
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