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p-Adic Valued Distributions in Mathematical Physics

  • Book
  • © 1994

Overview

Authors:
  1. Andrei Khrennikov

    1. Moscow Institute of Electronic Engineering, Zelenograd (Moscow), Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 309)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvi
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  2. First Steps to Non-Archimedean

    • Andrei Khrennikov
    Pages 1-29

  3. The Gauss, Lebesgue and Feynman Distributions Over Non-Archimedean Fields

    • Andrei Khrennikov
    Pages 31-64

  4. The Gauss and Feynman Distributions on Infinite-Dimensional Spaces over Non-Archimedean Fields

    • Andrei Khrennikov
    Pages 65-83

  5. Quantum Mechanics for Non-Archimedean Wave Functions

    • Andrei Khrennikov
    Pages 85-105

  6. Functional Integrals and the Quantization of Non-Archimedean Models with an Infinite Number of Degrees of Freedom

    • Andrei Khrennikov
    Pages 107-114

  7. The p-Adic-Valued Probability Measures

    • Andrei Khrennikov
    Pages 115-159

  8. Statistical Stabilization with Respect to p-adic and Real Metrics

    • Andrei Khrennikov
    Pages 161-191

  9. The p-adic Valued Probability Distributions (Generalized Functions)

    • Andrei Khrennikov
    Pages 193-213

  10. p-Adic Superanalysis

    • Andrei Khrennikov
    Pages 215-234

  11. Back Matter

    Pages 235-264
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Keywords

About this book

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

Authors and Affiliations

  • Moscow Institute of Electronic Engineering, Zelenograd (Moscow), Russia

    Andrei Khrennikov

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