From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory

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dc.creatorConnes, Alain
dc.creatorMarcolli, Matilde
dc.date2004-11-11
dc.date.accessioned2026-07-07T04:17:45Z
dc.date.available2026-07-07T04:17:45Z
dc.descriptionWe establish a precise relation between Galois theory in its motivic form with the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimensional regularization). We identify, through a Riemann-Hilbert correspondence based on the Birkhoff decomposition and the t'Hooft relations, a universal symmetry group (the "cosmic Galois group" suggested by Cartier), which contains the renormalization group and acts on the set of physical theories. This group is closely related to motivic Galois theory. We construct a universal singular frame of geometric nature, in which all divergences disappear. The paper includes a detailed overview of the work of Connes-Kreimer and background material on the main quantum field theoretic and algebro-geometric notions involved. We give a complete account of our results announced in math.NT/0409306.
dc.description97 pages LaTeX, 17 eps figures
dc.identifierhttps://arxiv.org/abs/hep-th/0411114
dc.identifierhttp://arxiv.org/abs/hep-th/0411114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/52886
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subjectQuantum Algebra
dc.titleFrom Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
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