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Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models

  • Book
  • © 1997

Overview

Authors:
  1. Andrei Khrennikov

    1. Moscow Institute of Electronic Engineering, Moscow, Russia
      Ruhr-University, Bochum, Germany
      Rikkyo University, Tokyo, Japan
      Växjö University, Sweden

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Part of the book series: Mathematics and Its Applications (MAIA, volume 427)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Measurements and Numbers

    • Andrei Khrennikov
    Pages 1-41

  3. Fundamentals

    • Andrei Khrennikov
    Pages 43-100

  4. Non-Archimedean Analysis

    • Andrei Khrennikov
    Pages 101-129

  5. The Ultrametric Hilbert Space Description of Quantum Measurements with Finite Precision

    • Andrei Khrennikov
    Pages 131-167

  6. Non-Kolmogorov Probability Theory

    • Andrei Khrennikov
    Pages 169-219

  7. Non-Kolmogorov Probability and Quantum Physics

    • Andrei Khrennikov
    Pages 221-247

  8. Position and Momentum Representations

    • Andrei Khrennikov
    Pages 249-282

  9. p-adic Dynamical Systems with Applications to Biology and Social Sciences

    • Andrei Khrennikov
    Pages 283-328

  10. Back Matter

    Pages 329-374
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Keywords

About this book

N atur non facit saltus? This book is devoted to the fundamental problem which arises contin­ 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 num­ 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.

Authors and Affiliations

  • Moscow Institute of Electronic Engineering, Moscow, Russia

    Andrei Khrennikov

  • Ruhr-University, Bochum, Germany

    Andrei Khrennikov

  • Rikkyo University, Tokyo, Japan

    Andrei Khrennikov

  • Växjö University, Sweden

    Andrei Khrennikov

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