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Non-Archimedean Analysis : Quantum Paradoxes, Dynamical Systems and Biological Models - Andrei Y. Khrennikov

Non-Archimedean Analysis

Quantum Paradoxes, Dynamical Systems and Biological Models

Hardcover Published: 30th September 1997
ISBN: 9780792348009
Number Of Pages: 376

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N atur non facit saltus? This book is devoted to the fundamental problem which arises continĀ­ uously in the process of the human investigation of reality: the role of a mathematical apparatus in a description of reality. We pay our main attention to the role of number systems which are used, or may be used, in this process. We shall show that the picture of reality based on the standard (since the works of Galileo and Newton) methods of real analysis is not the unique possible way of presenting reality in a human brain. There exist other pictures of reality where other numĀ­ ber fields are used as basic elements of a mathematical description. In this book we try to build a p-adic picture of reality based on the fields of p-adic numbers Qp and corresponding analysis (a particular case of so called non-Archimedean analysis). However, this book must not be considered as only a book on p-adic analysis and its applications. We study a much more extended range of problems. Our philosophical and physical ideas can be realized in other mathematical frameworks which are not obliged to be based on p-adic analysis. We shall show that many problems of the description of reality with the aid of real numbers are induced by unlimited applications of the so called Archimedean axiom.

Introduction
Measurements and Numbersp. 1
Fundamentalsp. 43
Non-Archimedean Analysisp. 101
The Ultrametric Hilbert Space Description of Quantum Measurements with a Finite Exactnessp. 131
Non-Kolmogorov Probability Theoryp. 169
Non-Kolmogorov Probability and Quantum Physicsp. 221
Position and Momentum Representationsp. 249
p-adic Dynamical Systems with Applications to Biology and Social Sciencesp. 283
Open Problemsp. 329
Newton's Method (Hensel Lemma)p. 331
Non-Real Realityp. 332
p-adic Description of the Black Body Radiationp. 336
p-adic Probability Justification of Dirac's Relativistic Quantization of Photonsp. 339
Quantum Mechanics of Vladimirov and Volovichp. 341
Bibliographyp. 345
Indexp. 369
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792348009
ISBN-10: 0792348001
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 376
Published: 30th September 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 3.05
Weight (kg): 1.61