Renormalization, the Riemann-Hilbert correspondence, and motivic galois theory

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]. © 2007 Springer.