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Number Theory and Physics

Proceedings of the Winter School, Les Houches, France, March 7–16, 1989

  • Conference proceedings
  • © 1990

Overview

Editors:
  1. Jean-Marc Luck

    1. Service de Physique Théorique, C.E.N Saclay, Gif-sur-Yvette Cedex, France

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  2. Pierre Moussa

    1. Service de Physique Théorique, C.E.N Saclay, Gif-sur-Yvette Cedex, France

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  3. Michel Waldschmidt

    1. Institut Henri-Poincaré, Problèmes Diophantiens, Université de Paris 6, Paris Cedex 05, France

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Part of the book series: Springer Proceedings in Physics (SPPHY, volume 47)

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Table of contents (32 papers)

  1. Front Matter

    Pages I-XIII
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  2. Conformally Invariant Field Theories, Integrability, Quantum Groups

    1. Front Matter

      Pages 1-1
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    2. Z/NZ Conformal Field Theories

      • P. Degiovanni
      Pages 2-19

    3. Affine Characters and Modular Transformations

      • M. Bauer, C. Itzykson
      Pages 20-32

    4. Conformal Field Theory on a Riemann Surface

      • H. Ooguri
      Pages 33-43

    5. Modular Invariance of Field Theories and String Compactifications

      • A. Shapere
      Pages 44-55

    6. Yang-Baxter Algebras and Quantum Groups

      • H. J. de Vega
      Pages 56-67

    7. Representations of Uq sl(2) for q a Root of Unity

      • H. Saleur
      Pages 68-76

  4. Spectral Problems, Automata and Substitutions

    1. Front Matter

      Pages 139-139
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    2. Spectral Properties of Schrödinger’s Operator with a Thue-Morse Potential

      • J. Bellissard
      Pages 140-150

    3. On the Non-commutative Torus of Real Dimension Two

      • P. Cohen
      Pages 151-156

    4. Topological Invariants Associated with Quasi-Periodic Quantum Hamiltonians

      • H. Kunz
      Pages 157-161

    5. Spectra of Some Almost Periodic Operators

      • A. Sütö
      Pages 162-169
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Keywords

About this book

7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu­ tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p­ adic numbers in a remarkable way.

Editors and Affiliations

  • Service de Physique Théorique, C.E.N Saclay, Gif-sur-Yvette Cedex, France

    Jean-Marc Luck, Pierre Moussa

  • Institut Henri-Poincaré, Problèmes Diophantiens, Université de Paris 6, Paris Cedex 05, France

    Michel Waldschmidt

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