Causality: The p-adic Theory

by Vladimir Anashin

Overview

This book delves into the mathematical theory of causal functions over discrete time, offering a fresh perspective on causality beyond its philosophical roots. By exploring the intricate world of p-adic 1-Lipschitz functions, this volume bridges the gap between abstract mathematical concepts and their practical applications in fields such as automata theory, combinatorics, and applied computer science.

Readers will uncover a wealth of insights as the book investigates key topics including the nature of causal functions, the role of discrete time in causality, and the application of non-Archimedean metrics. With contributions from eminent scholars, this work invites readers to ponder critical questions: How do we define causality in mathematical terms? What are the implications of using p-adic analysis in understanding complex systems especially quantum ones? The author's unique approach makes this book an essential read for anyone interested in the intersection of mathematics and real-world applications.

Ideal for researchers and practitioners with a background in mathematics, computer science, or physics, this book is a valuable resource for those seeking to deepen their understanding of causal functions. Whether you're a scholar exploring theoretical perspectives or a professional looking to apply these concepts practically, this volume offers a comprehensive guide to navigating the complexities of causality. Part of an ongoing series on advanced mathematical theories, it is an indispensable addition to any academic library.

Product Details

ISBN-13:	9783031858178
Publisher:	Springer Nature Switzerland
Publication date:	04/25/2025
Series:	STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Pages:	413
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Vladimir S. Anashin is a Professor of Mathematics at Lomonosov Moscow State University and a Leading Research Fellow at Federal Research Center ‘Computer Science and Control’ of the Russian Academy of Sciences, Russia. His research interests include non-Archimedean analysis, automata theory, ring theory, group theory as well as applications to computer science and foundations of physics. As a leading expert in the p-adic theory of automata and its applications to computer science and interpretation of quantum mechanics, Prof. Anashin was awarded visiting professorship of Université de Picardie Jules Verne, France (2007) and visiting professorship for Senior International Scientists, Chinese Academy of Sciences (2010-2014), also he was recognized as a Distinguished Lecturer by National Centre of Mathematics and Interdiciplinary Sciences, China (2011).

Table of Contents

Foreword.- Preface.- Background.- Part I. Basics of p-Adic Analysis.- Rings and Fields of p-Adic Numbers.- p-Adic Calculus.- p-Adic Series.- 1-Lipschitz functions.- Special Classes of 1-Lipschitz Functions.- Part II. The p-Adic Ergodic Theory.- Ergodic Theory: Preliminaries for the p-Adic Case.- The Main Ergodic Theorem for p-Adic 1-Lipschitz Maps.- 1-Lipschitz Ergodicity on Zp.- Measure-Preservation and Ergodicity of Uniformly Differentiable Functions.- 1-Lipschitz Ergodicity on Subspaces.- Plots of 1-Lipschitz Functions in Euclidean Space.- Part III. Applications.- Applications to Automata Theory.- Applications to Computer Science.- Application to Combinatorics.- Applications to Foundations of Quantum Theory.- References.- Index.