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Frontiers in Number Theory, Physics, and Geometry II

On Conformal Field Theories, Discrete Groups and Renormalization

  • Book
  • © 2007

Overview

Editors:
  1. Pierre Cartier

    1. I.H.E.S., Bures-sur-Yvette, France

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  2. Pierre Moussa

    1. Service de Physique Théorique, CEA/Saclay, Gif-sur-Yvette, France

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  3. Bernard Julia

    1. LPTENS, Paris, France

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  4. Pierre Vanhove

    1. Service de Physique Théorique, CEA/Saclay, Gif-sur-Yvette, France

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  • very distinguished international list of authors including Alain Connes, a Fields Medallist ...

  • Cutting-edge research in well-written expository form

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XXVIII
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  2. Conformal Field Theories for Strings and Branes

    1. Front Matter

      Pages I-XXVIII
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    2. The Dilogarithm Function

      • Don Zagier
      Pages 3-65

    3. Conformal Field Theory and Torsion Elements of the Bloch Group

      • Werner Nahm
      Pages 67-132

    4. Tracks, Lie's, and Exceptional Magic

      • Predrag Cvitanović
      Pages 133-160

    5. Gauge Theories from D Branes

      • Paolo Di Vecchia, Antonella Liccardo
      Pages 161-222

    6. On Superconformal Field Theories Associated to Very Attractive Quartics

      • Katrin Wendland
      Pages 223-244

  3. Discrete Groups and Automorphic Forms

    1. Front Matter

      Pages I-XXVIII
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    2. An Introduction to Arithmetic Groups

      • Christophe Soulé
      Pages 247-276

    3. Automorphic Forms: A Physicist's Survey

      • Boris Pioline, Andrew Waldron
      Pages 277-302

    4. Strings and Arithmetic

      • Gregory Moore
      Pages 303-359

    5. Modular Curves, C*-algebras, and Chaotic Cosmology

      • Matilde Marcolli
      Pages 361-372

    6. Replicable Functions: An Introduction

      • John McKay, Abdellah Sebbar
      Pages 373-386

    7. Lectures on the Langlands Program and Conformal Field Theory

      • Edward Frenkel
      Pages 387-533

  4. Hopf Algebras and Renormalization

    1. Front Matter

      Pages I-XXVIII
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    2. A Primer of Hopf Algebras

      • Pierre Cartier
      Pages 537-615

    3. Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory

      • Alain Connes, Matilde Marcolli
      Pages 617-713

    4. Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities

      • Dirk Kreimer
      Pages 715-736

    5. Algebraic Algorithms in Perturbative Calculations

      • Stefan Weinzierl
      Pages 737-757

    6. Multiple Logarithms, Algebraic Cycles and Trees

      • H. Gangl, A.B. Goncharov, A. Levin
      Pages 759-774
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Keywords

Editors and Affiliations

  • I.H.E.S., Bures-sur-Yvette, France

    Pierre Cartier

  • Service de Physique Théorique, CEA/Saclay, Gif-sur-Yvette, France

    Pierre Moussa, Pierre Vanhove

  • LPTENS, Paris, France

    Bernard Julia

Bibliographic Information

  • Book Title: Frontiers in Number Theory, Physics, and Geometry II

  • Book Subtitle: On Conformal Field Theories, Discrete Groups and Renormalization

  • Editors: Pierre Cartier, Pierre Moussa, Bernard Julia, Pierre Vanhove

  • DOI: https://doi.org/10.1007/978-3-540-30308-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Hardcover ISBN: 978-3-540-30307-7Published: 06 December 2006

  • Softcover ISBN: 978-3-642-06776-1Published: 12 February 2010

  • eBook ISBN: 978-3-540-30308-4Published: 18 July 2007

  • Edition Number: 1

  • Number of Pages: XXVIII, 789

  • Number of Illustrations: 23 b/w illustrations

  • Topics: Number Theory, Algebraic Geometry, Theoretical, Mathematical and Computational Physics

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