p-adic valued distributions in mathematical physics
Author(s)
Bibliographic Information
p-adic valued distributions in mathematical physics
(Mathematics and its applications, v. 309)
Kluwer Academic Publishers, c2010
- : [pbk.]
Available at 2 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. [249]-261) and index
Description and Table of Contents
Description
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.
Table of Contents
Introduction. I. First Steps to Non-Archimedean Fields. 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. Appendix: 1. Expansion of Numbers on a Given Scale. 2. An Analogue of Newton's Method. 3. Non-Existence of Differential Maps from Qp to R. Bibliography. Index.
by "Nielsen BookData"