Number Theory and Physics: Proceedings of the Winter School, Les Houches, France, March 7?16, 1989 (Springer Proceedings in Physics).

Luck, J.-M.:

ISBN 10: 3540521291 / ISBN 13: 9783540521297

Edité par Berlin: Springer, 1990

A propos de cet article

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Détails bibliographiques

• Titre: Number Theory and Physics: Proceedings of the Winter School, Les Houches, France, March 7?16, 1989 (Springer Proceedings in Physics).
• Éditeur: Berlin: Springer
• Date de parution: 1990
• Langue: anglais
• ISBN à 10 chiffres: 3540521291
• ISBN à 13 chiffres: 9783540521297
• Reliure: Karton Karton
• État de l'article: Sehr gut
• Poids: 646 grammes
• Catalogues du vendeur:
  • Mathematik

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

The contributions to this book can be divided into two categories: those in which mathematicians write on problems relevant to theoretical physics, and those dealing with problems relevant to number theory, written by physicists. Many recent developments in theoretical physics display aspects related to number theory, and this cooperation will be furthered by this volume. The authors from each discipline have taken pains to present their contributions in a manner that is attractive and understandable to readers from the other discipline. The subjects covered include: modular forms and applications to quantum field theory for strings, number theoretical aspects of the spectra of operators applied to the Hall effect, quasicrystals, almost periodic systems, the Riemann zeta function, applications of number theory to dynamical systems, statistical mechanics, lattices, stochastic processes and integrable systems.