Combinatorics and Physics
About this Title
Kurusch Ebrahimi-Fard, Matilde Marcolli and Walter D. van Suijlekom, Editors
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.
Graduate students and research mathematicians interested in applications of combinatorics to physics.
Table of Contents
- Christian Brouder and Frédéric Patras – One-particle irreducibility with initial correlations [MR 2790299]
- Francis Brown – Multiple zeta values and periods: from moduli spaces to Feynman integrals [MR 2790300]
- Frédéric Chapoton and Alessandra Frabetti – From quantum electrodynamics to posets of planar binary trees [MR 2790301]
- Gérard H. E. Duchamp and Christophe Tollu – Sweedler’s duals and Schützenberger’s calculus [MR 2790302]
- L. Foissy – Primitive elements of the Hopf algebra of free quasi-symmetric functions [MR 2790303]
- Roland Friedrich – A renormalisation group approach to stochastic Lœwner evolutions [MR 2790304]
- José M. Gracia-Bondía – On the causal gauge principle [MR 2790305]
- Massimiliano Gubinelli – Abstract integration, combinatorics of trees and differential equations [MR 2790306]
- Ralf Holtkamp – Rooted trees appearing in products and co-products [MR 2790307]
- Arieh Iserles – Magnus expansions and beyond [MR 2790308]
- T. Krajewski and P. Martinetti – Wilsonian renormalization, differential equations and Hopf algebras [MR 2790309]
- E. Kraus – Algebraic analysis of non-renormalization theorems in supersymmetric field theories [MR 2790310]
- Dirk Kreimer – Not so non-renormalizable gravity [MR 2790311]
- Dominique Manchon – Renormalised multiple zeta values which respect quasi-shuffle relations [MR 2790312]
- Frédéric Menous – Formulas for the Connes-Moscovici Hopf algebra [MR 2790313]
- Ângela Mestre and Robert Oeckl – Hopf algebras and the combinatorics of connected graphs in quantum field theory [MR 2790314]
- Alexander Lundervold and Hans Munthe-Kaas – Hopf algebras of formal diffeomorphisms and numerical integration on manifolds [MR 2790315]
- D. Oriti – A combinatorial and field theoretic path to quantum gravity: the new challenges of group field theory [MR 2790316]
- Sylvie Paycha – Noncommutative formal Taylor expansions and second quantised regularised traces [MR 2790317]
- Abhijnan Rej – Motives: an introductory survey for physicists [MR 2790318]
- Walter D. van Suijlekom – Combinatorics and Feynman graphs for gauge theories [MR 2790319]
- Fabien Vignes-Tourneret – Multi-scale analysis and non-commutative field theory [MR 2790320]