Published November 11, 2004
| Submitted
Discussion Paper
Open
From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
- Creators
- Connes, Alain
-
Marcolli, Matilde
Chicago
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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–Hilbert 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].
Additional Information
(Submitted on 11 Nov 2004) We are very grateful to Jean–Pierre Ramis for many useful comments on an early draft of this paper, for the kind invitation to Toulouse, and for the many stimulating discussions we had there with him, Frédéric Fauvet, and Laurent Stolovitch. We thank Frédéric Menous and Giorgio Parisi for some useful correspondence. Many thanks go to Dirk Kreimer, whose joint work with AC on perturbative renormalization is a main topic of this Chapter.Attached Files
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Additional details
- Eprint ID
- 79059
- Resolver ID
- CaltechAUTHORS:20170713-080604764
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