Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory
Identifieur interne : 000946 ( Main/Exploration ); précédent : 000945; suivant : 000947Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory
Auteurs : Alain Connes [France] ; Matilde Marcolli [Allemagne]Source :
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].
Url:
DOI: 10.1007/978-3-540-30308-4_13
Affiliations:
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