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El. knyga: p-Adic Valued Distributions in Mathematical Physics

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A study of non-Archimedean, and especially p -adic mathematical physics. Basic questions about the nature and possible applications of such a theory are investigated. Interesting physical models are developed like the p -adic universe, where distances can be infinitely large p -adic numbers, energies, and momentum. Two types of measurement algorithms are shown to exist, one generating real values and one generating p -adic values. The mathematical basis for the theory is a well developed non-Archimedean analysis, and subjects that are treated include non-Archimedean valued distributions using analytic test functions, and Gaussian and Feynman non-Archimedean distributions. Annotation copyright Book News, Inc. Portland, Or.

This book is devoted to the study of non-Archimedean, and especially p-adic mathematical physics. Basic questions about the nature and possible applications of such a theory are investigated. Interesting physical models are developed like the p-adic universe, where distances can be infinitely large p-adic numbers, energies and momentums. Two types of measurement algorithms are shown to exist, one generating real values and one generating p-adic values. The mathematical basis for the theory is a well developed non-Archimedean analysis, and subjects that are treated include non-Archimedean valued distributions using analytic test functions, Gaussian and Feynman non-Archimedean distributions with applications to quantum field theory, differential and pseudo-differential equations, infinite-dimensional non-Archimedean analysis, and p-adic valued theory of probability and statistics.
This volume will appeal to a wide range of researchers and students whose work involves mathematical physics, functional analysis, number theory, probability theory, stochastics, statistical physics or thermodynamics.
I First Steps to Non-Archimedean.- II The Gauss, Lebesgue and Feynman
Distributions Over Non-Archimedean Fields.- III The Gauss and Feynman
Distributions on Infinite-Dimensional Spaces over Non-Archimedean Fields.- IV
Quantum Mechanics for Non-Archimedean Wave Functions.- V Functional Integrals
and the Quantization of Non-Archimedean Models with an Infinite Number of
Degrees of Freedom.- VI The p-Adic-Valued Probability Measures.- VII
Statistical Stabilization with Respect to p-adic and Real Metrics.- VIII The
p-adic Valued Probability Distributions (Generalized Functions).- IX p-Adic
Superanalysis.- Bibliographical Remarks.- Open Problems.-
1. Expansion of
Numbers in a Given Scale.-
2. An Analogue of Newtons Method.
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