Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization

ISBN-13: 9783642067761 / Angielski / Miękka / 2010 / 820 str.

Pierre Cartier; Bernard Julia; Pierre Moussa

Opis

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

Spis treści

Part I: Conformal Field Theory. E. Frenkel: Lectures on the Langlands Program and Conformal Field Theory.- W. Nahm: Conformal Field Theory and Torsion Elements of the Bloch Group.- P. Cvitanovic: Tracks, Lie’s, and Exceptional Magic.- P. Di Vecchia/A. Liccardo: Gauge Theories from D. Branes.- K. Wendland: On Superconformal Field Theories Associated to Very Attractive Quartics.- Part II: Discrete Groups. C. Soulé: An Introduction to Arithmetic Groups.- B. Pioline/A. Waldron: Automorphic Forms: A Physicist’s Survey.- J. McKay/A. Sebbar: Replicable Functions: An Introduction.- D. Zagier: The Dilogarithm Function in Geometry and Number Theory.- H. Gangl/A.B.Goncharov/A. Levin: Multiple Logarithms, Algebraic Cycles and Trees.- M. Marcolli: Modular Curves, C-Algebras and Chaotic Cosmology.- G. Moore: Strings and Arithmetic.- Part III: Renormalization. A. Connes/M. Marcolli: Renormalization, The Riemann-Hilbert correspondence, and Motivic Galois Theory.- D. Kreimer: Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities.- S. Weinzierl: Algebraic Algorithms in Perturbative Calculations.