Overview

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.Contents: Analysis on the Field p-Adic Numbers: The Field of p-Adic NumbersAnalytic FunctionsAdditive and Multiplicative CharactersIntegration TheoryThe Gaussian IntegralsGeneralized FunctionsConvolution and the Fourier TransformationHomogeneous Generalized Functions Pseudo-Differential Operators on the Field of p-Adic Numbers: The Operator D?p-Adic Schrodinger Operators p-Adic Quantum Theory: p-Adic Quantum MechanicsSpectral Theory in p-Adic Quantum MechanicsWeyl Systems. Infinite Dimensional Casep-Adic Stringsq-Analysis (Quantum Groups) and p-Adic AnalysisStochastic Processes Over the Field of p-Adic NumbersReadership: Students, postgraduates, mathematical physicists, mathematicians and physicists.

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9781299671010

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