Overview

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.

Full Product Details

Author:   Andrei Y. Khrennikov
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 1994
Volume:   309
Dimensions:   Width: 16.00cm , Height: 1.50cm , Length: 24.00cm
Weight:   0.454kg
ISBN:  

9789048144761

ISBN 10:   9048144760
Pages:   264
Publication Date:   03 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

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 Newton’s Method.

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