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From Number Theory to Physics
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Recent developments in Physics have involved many questions related to Number Theory, in an increasingly direct way. This trend is especially visible in two broad families of problems, namely, conformally invariant two-dimensional field theories, completely integrable models, and the string theory of fundamental interactions on the one hand, and on the other hand the theory of dynamical systems, classical and quantum chaos, incommensurate structures and quasicrystals. The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagocical viewpoint dealing with the topics of elliptic curves, modular forms, Zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. §Others again report on applications of number theory to physical problems including classical and quantum dynamical systems, periodic and quasiperiodic lattices.
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