Research Catalog

Title

Non-Archimedean analysis : quantum paradoxes, dynamical systems, and biological models / by Andrei Khrennikov.

Author

Khrennikov, A. I︠U︡. (Andreĭ I︠U︡rʹevich), 1958-

Publication

Dordrecht ; Boston : Kluwer Academic Publishers, ©1997.

Items in the Library & Off-site

Details

Description

xvii, 371 pages; 25 cm

Summary

This work can be recommended as an extensive course on p-adic mathematics, treating subjects such as a p-adic theory of probability and stochastic processes; spectral theory of operators in non-Archimedean Hilbert spaces; dynamic systems; p-adic fractal dimension, infinite-dimensional analysis and Feynman integration based on the Albeverio-Hoegh-Krohn approach; both linear and nonlinear differential and pseudo-differential equations; complexity of random sequences and a p-adic description of chaos. Also, the present volume explores the unique concept of using fields of p-adic numbers and their corresponding non-Archimedean analysis, a p-adic solution of paradoxes in the foundations of quantum mechanics, and especially the famous Einstein-Podolsky-Rosen paradox to create an epistemological framework for scientific use. This book will be valuable to postgraduate students and researchers with an interest in such diverse disciplines as mathematics, physics, biology and philosophy.

Series Statement

Mathematics and its applications ; v. 427

Uniform Title

Mathematics and its applications (Kluwer Academic Publishers) ; v. 427.

Subject

• Quantum theory
• Physical measurements
• p-adic analysis
• Hilbert space
• Reality
• Systèmes dynamiques
• Biométrie
• Sociométrie

Bibliography (note)

• Includes bibliographical references (p. [345]-368) and index.

Contents

I. Measurements and Numbers -- II. Fundamentals -- III. Non-Archimedean Analysis -- IV. The Ultrametric Hilbert Space Description of Quantum Measurements with a Finite Exactness -- V. Non-Kolmogorov Probability Theory -- VI. Non-Kolmogorov Probability and Quantum Physics -- VII. Position and Momentum Representations -- VIII. p-adic Dynamical Systems with Applications to Biology and Social Sciences -- Open Problems -- App. 1. Newton's Method (Hensel Lemma) -- App. 2. Non-Real Reality -- App. 3. p-adic Description of the Black Body Radiation -- App. 4. p-adic Probability Justification of Dirac's Relativistic Quantization of Photons -- App. 5. Quantum Mechanics of Vladimirov and Volovich.

ISBN

• 0792348001
• 9780792348009

LCCN

97031467

OCLC

• ocm37546646
• 37546646
• SCSB-8805943

Owning Institutions

Princeton University Library