04467nam 2200625 450 991078863380332120220823061203.00-8218-8218-X(CKB)3240000000070062(EBL)3113301(SSID)ssj0000629268(PQKBManifestationID)11425381(PQKBTitleCode)TC0000629268(PQKBWorkID)10717932(PQKB)10612968(MiAaPQ)EBC3113301(RPAM)16578399(PPN)197108687(EXLCZ)99324000000007006220101214h20112011 uy| 0engur|n|---|||||txtccrCombinatorics 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, editorsProvidence, Rhode Island :American Mathematical Society,[2011]©20111 online resource (480 p.)Contemporary mathematics,5390271-4132Description based upon print version of record.0-8218-5329-5 Includes bibliographical references.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 Weinberg's alam 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 Connes-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.Contemporary mathematics (American Mathematical Society).5390271-4132Renormalization groupCongressesQuantum field theoryCongressesNumerical integrationCongressesRenormalization groupQuantum field theoryNumerical integration530.14/381T1565D30mscEbrahimi-Fard Kurusch1973-Marcolli MatildeSuijlekom Walter D. van.1978-Max-Planck-Institut für Mathematik,Conference on Combinatorics and Physics(2007 :Max Planck Institut für Mathematik),MiAaPQMiAaPQMiAaPQBOOK9910788633803321Combinatorics and physics763454UNINA