Combinatorics and Physics

This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Author Biography:
Kurusch Ebrahimi-Fard, Universidad de Zaragoza, Spain. Matilde Marcolli, California Institute of Technology, Pasadena, CA. Walter D. van Suijlekom, Radboud University Nijmegen, The Netherlands


Contents:
One-particle irreducibility with initial correlations by C. Brouder and F. Patras
Multiple zeta values and periods: From moduli spaces to Feynman integrals by F. Brown
From quantum electrodynamics to posets of planar binary trees by F. Chapoton and A. Frabetti
Sweedler's duals and Schutzenberger's calculus by G. H. E. Duchamp and C. Tollu
Primitive elements of the Hopf algebra of free quasi-symmetric functions by L. Foissy
A Renormalisation Group approach to Stochastic Loewner Evolutions by R. Friedrich
On the causal gauge principle by J. M. Gracia-Bondia
Abstract integration, combinatorics of trees and differential equations by M. Gubinelli
Rooted trees appearing in products and co-products by R. Holtkamp
Magnus expansions and beyond by A. Iserles
Wilsonian renormalization, differential equations and Hopf algebras by T. Krajewski and P. Martinetti
Algebraic analysis of non-renormalization theorems in supersymmetric field theories by E. Kraus
Not so non-renormalizable gravity by D. Kreimer
Renormalised multiple zeta values which respect quasi-shuffle relations by D. Manchon
Formulas for the Connes-Moscovici Hopf algebra by F. Menous
Hopf algebras and the combinatorics of connected graphs in quantum field theory by A. Mestre and R. Oeckl
Hopf algebras of formal diffeomorphisms and numerical integration on manifolds by A. Lundervold and H. Munthe-Kaas
A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory by D. Oriti
Noncommutative formal Taylor expansions and second quantised regularised traces by S. Paycha
Motives: An introductory survey for physicists by A. Rej
Combinatorics and Feynman graphs for gauge theories by W. van Suijlekom Multi-scale analysis and non-commutative field theory by F. Vignes-Tourneret