/ 05 04 08 5 v 1 9 A pr 2 00 5 QUANTUM FIELDS AND MOTIVES

ar X iv : h ep - t h / 05 04 08 5 v 1 9 A pr 2 00 5 QUANTUM FIELDS AND MOTIVES

The main idea of renormalization is to correct the original Lagrangian of a quantum field theory by an infinite series of counterterms, labelled by the Feynman graphs that encode the combinatorics of the perturbative expansion of the theory. These counterterms have the effect of cancelling the ultraviolet divergences. Thus, in the procedure of perturbative renormalization, one introduces a coun...

Mixed Artin–Tate motives over number rings

This paper studies Artin–Tate motives over bases S ⊂ Spec OF , for a number field F . As a subcategory of motives over S, the triangulated category of Artin–TatemotivesDATM(S) is generated by motives φ∗1(n), where φ is any finite map. After establishing the stability of these subcategories under pullback and pushforward along open and closed immersions, a motivic t-structure is constructed. Exa...

Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields

We explain work on the arithmetic of Gamma and Zeta values for function fields. We will explore analogs of the gamma and zeta functions, their properties, functional equations, interpolations, their special values, their connections with periods of Drinfeld modules and t-motives, algebraic relations they satisfy and various methods showing that there are no more relations between them. We also ...

Motivic structures in quantum field theory

This is a writeup of the lecture given by the author at the StringMath 2011 conference in Philadelphia. It gives an overview of recent work of the author, in collaboration with Aluffi and with Ceyhan, on some aspects of the occurrence of motivic structures in perturbative quantum field theory. 1. Motives and qnant.nm fields The theory of motives originated with Grothendieck's idea of a "univers...

Noncommutative Geometry, Quantum Fields and Motives