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

Name: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models
Author: Andrei Y. Khrennikov
ISBN: 9789401071642

by Andrei Y. Khrennikov

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Overview

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.

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Editorials

Booknews

Khrennikov (Moscow Institute of Electronic Engineering) provides a course in

-adic mathematics for advanced students and researchers in math, physics, biology, and philosophy. Major topic headings encompass: fundamentals, non-Kolmogorov probability and quantum physics, position and momentum representations,

-adic dynamical systems with applications to biology and social sciences, and open problems in the field. A unique application of non-Archimedean solutions (e.g. to paradoxes in the foundations of quantum mechanics) is to create an epistemological framework for scientific use. Annotation c. by Book News, Inc., Portland, Or.