p-Adic Valued Distributions in Mathematical Physics / Edition 1

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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, shastics, statistical physics or thermodynamics.

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Product Details

  • ISBN-13: 9789048144761
  • Publisher: Springer Netherlands
  • Publication date: 12/2/2010
  • Series: Mathematics and Its Applications (closed) Series, #309
  • Edition description: Softcover reprint of hardcover 1st ed. 1994
  • Edition number: 1
  • Pages: 264
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.60 (d)

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.

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