Hopf Algebras, Renormalization and Noncommutative Geometry
نویسندگان
چکیده
منابع مشابه
Hopf Algebras, Renormalization and Noncommutative Geometry
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations.
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We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic coh...
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In 1999, A. Connes and D. Kreimer have discovered the Hopf algebra structure on the Feynman graphs of scalar field theory. They have found that the renormalization can be interpreted as a solving of some Riemann — Hilbert problem. In this work a generalization of their scheme to the case of quantum electrodynamics is proposed. The action of the gauge group on the Hopf algebra of diagrams are de...
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These are the notes of five lectures given at the Summer School Geometric and Topological Methods for Quantum Field Theory , held in Villa de Leyva (Colombia), July 2–20, 2007. The lectures are meant for graduate or almost graduate students in physics or mathematics. They include references, many examples and some exercices. The content is the following. The first lecture is a short introductio...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1998
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050499