Diffusion, Quantum Theory, and Radically Elementary Mathematics
eBook - PDF

Diffusion, Quantum Theory, and Radically Elementary Mathematics

  1. 257 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Diffusion, Quantum Theory, and Radically Elementary Mathematics

About this book

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians.


The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

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Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1. Introduction: Diffusive Motion and Where It Leads
  7. Chapter 2. Hypercontractivity, Logarithmic Sobolev Inequalities, and Applications: A Survey of Surveys
  8. Chapter 3. Ed Nelson's Work in Quantum Theory
  9. Chapter 4. Symanzik, Nelson, and Self-Avoiding Walk
  10. Chapter 5. Stochastic Mechanics: A Look Back and a Look Ahead
  11. Chapter 6. Current Trends in Optimal Transportation: A Tribute to Ed Nelson
  12. Chapter 7. Internal Set Theory and Infinitesimal Random Walks
  13. Chapter 8. Nelson's Work on Logic and Foundations and Other Reflections on the Foundations of Mathematics
  14. Chapter 9. Some Musical Groups: Selected Applications of Group Theory in Music
  15. Chapter 10. Afterword
  16. Appendix A. Publications by Edward Nelson
  17. Index

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Yes, you can access Diffusion, Quantum Theory, and Radically Elementary Mathematics by William G. Faris, William Faris in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebraic Geometry. We have over one million books available in our catalogue for you to explore.