Combinatorics and physics : Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany / / Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, editors

• Record Nr.: UNINA9910480290103321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2011]; ©2011
• ISBN: 0-8218-8218-X
• Descrizione fisica: 1 online resource (480 p.)
• Collana: Contemporary mathematics ; ; volume 539
• Disciplina: 530.14/3
• Soggetti: Renormalization group; Quantum field theory; Numerical integration; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Preface""; ""List of participants""; ""One-particle irreducibility with initial correlations""; ""Multiple zeta values and periods: From moduli spaces to Feynman integrals""; ""From quantum electrodynamics to posets of planar binary trees""; ""Sweedler's duals and Schutzenberger's calculus""; ""Primitive elements of the Hopf algebra of free quasi-symmetric functions""; ""A Renormalisation Group approach to Stochastic Loewner Evolutions""; ""On the causal gauge principle""; ""1. Introduction""; ""2. Overview of the CGI method""; ""3. The abelian model""; ""4. Three MVBs""; ""5. The Weinbergâ€?Salam model within CGI""""6. Discussion""; ""References""; ""Abstract integration, combinatorics of trees and differential equations""; ""Rooted trees appearing in products and co-products""; ""Magnus expansions and beyond""; ""Wilsonian renormalization, differential equations and Hopf algebras""; ""1. Introduction""; ""2. Basics of wilsonian renormalization""; ""3. Rooted trees and power series of non linear operators""; ""4. Renormalization, ; effective actions and Feynman diagrams""; ""5. Conclusion and outlook""; ""Acknowledgements""; ""References""; ""Algebraic analysis of non-renormalization theorems in supersymmetric field theories""""Not so non-renormalizable gravity""; ""Renormalised multiple zeta values which respect quasi-shuffle relations""; ""Formulas for the Connesâ€?Moscovici Hopf algebra""; ""Hopf algebras and the combinatorics of connected graphs in quantum field theory""; ""Hopf Algebras of Formal Diffeomorphisms and Numerical Integration on Manifolds""; ""A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory""; ""Noncommutative formal Taylor expansions and second quantised regularised traces""""Motives: An introductory survey for physicists""; ""1. Introduction""; ""2. The Grothendieck ring""; ""3. The Tannakian formalism""; ""4. Weil cohomology""; ""5. Classical motives""; ""6. Mixed motives""; ""7. Motivic measures and zeta functions""; ""Appendix A. Motivic ideas in physics (by M.Marcolli)""; ""References""; ""Combinatorics and Feynman graphs for gauge theories""; ""Multi-scale Analysis and Non-commutative Field Theory""