Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory

Alain Connes () and Matilde Marcolli ()
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Alain Connes: College de France
Matilde Marcolli: Max–Planck Institut für Mathematik

A chapter in Frontiers in Number Theory, Physics, and Geometry II, 2007, pp 617-713 from Springer

Abstract: Abstract We give here a comprehensive treatment of the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimensional regularization), in the framework of the Riemann–pHilbert correspondence and motivic Galois theory. We give a detailed overview of the work of Connes–Kreimer [31], [32]. We also cover some background material on affine group schemes, Tannakian categories, the Riemann–Hilbert problem in the regular singular and irregular case, and a brief introduction to motives and motivic Galois theory. We then give a complete account of our results on renormalization and motivic Galois theory announced in [35].

Keywords: Hopf Algebra; Galois Group; Group Scheme; Noncommutative Geometry; Hilbert Problem (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-30308-4_13

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DOI: 10.1007/978-3-540-30308-4_13

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