**Contemporary Mathematics**

Volume: 539;
2011;
465 pp;
Softcover

MSC: Primary 81; 65;

Print ISBN: 978-0-8218-5329-0

Product Code: CONM/539

List Price: $130.00

Individual Member Price: $104.00

**Electronic ISBN: 978-0-8218-8218-4
Product Code: CONM/539.E**

List Price: $130.00

Individual Member Price: $104.00

# Combinatorics and Physics

Share this page *Edited by *
*Kurusch Ebrahimi-Fard; Matilde Marcolli; Walter D. van Suijlekom*

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 für 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.

#### Table of Contents

# Table of Contents

## Combinatorics and Physics

- Contents v6 free
- Preface vii8 free
- List of participants ix10 free
- One-particle irreducibility with initial correlations 112 free
- Multiple zeta values and periods: From moduli spaces to Feynman integrals 2738
- From quantum electrodynamics to posets of planar binary trees 5364
- Sweedler's duals and Schutzenberger's calculus 6778
- Primitive elements of the Hopf algebra of free quasi-symmetric functions 7990
- A Renormalisation Group approach to Stochastic Loewner Evolutions 89100
- On the causal gauge principle 115126
- Abstract integration, combinatorics of trees and differential equations 135146
- Rooted trees appearing in products and co-products 153164
- Magnus expansions and beyond 171182
- Wilsonian renormalization, differential equations and Hopf algebras 187198
- Algebraic analysis of non-renormalization theorems in supersymmetric field theories 237248
- Not so non-renormalizable gravity 247258
- Renormalised multiple zeta values which respect quasi-shuffle relations 255266
- Formulas for the Connes–Moscovici Hopf algebra 269280
- Hopf algebras and the combinatorics of connected graphs in quantum field theory 287298
- Hopf Algebras of Formal Diffeomorphisms and Numerical Integration on Manifolds 295306
- A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory 325336
- Noncommutative formal Taylor expansions and second quantised regularised traces 349360
- Motives: An introductory survey for physicists 377388
- Combinatorics and Feynman graphs for gauge theories 417428
- Multi-scale Analysis and Non-commutative Field Theory 443454

#### Readership

Graduate students and research mathematicians interested in applications of combinatorics to physics.