Foundations of Quantum Theory
From Classical Concepts to Operator Algebras
Authors: Landsman, Klaas
Free Preview Integrates mathematical physics and the philosophy of physics in a unique way
 Relates the Copenhagen Interpretation of Bohr and Heisenberg to the operator algebras of von Neumann
 Proposes a new solution to the measurement problem of quantum mechanics based on deep conceptual and mathematical insights
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 About this book

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the KochenSpecker, Free Will, and Bell Theorems, the KadisonSinger conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
This book is Open Access under a CC BY licence.
 About the authors

Klaas Landsman (1963) obtained his PhD in Theoretical HighEnergy Physics from the University of Amsterdam in 1989. He was a research fellow at the University of Cambridge from 19891997, with a sojourn as Alexander von Humboldt Fellow in Hamburg from 199394. He was subsequently a Royal Academy Research Fellow at the University of Amsterdam from 19972002, and obtained a Pioneer Grant from NWO in 2002. Klaas has held the Chairs in Analysis and subsequently in Mathematical Physics at the Radboud University since 2004, and in 2011 was awarded the Bronze Medal of this university for his outreach work in mathematics. His research is mainly concerned with noncommutative geometry and with the mathematical foundations of quantum theory.
 Reviews

“Quantum theory has frequent applications in the subjects of quantum information theory and quantum optics. The purpose of this book is to present the foundations of quantum theory in connection with classical physics, from the point of view of classicalquantum duality. … This good book is recommended for mathematicians, physicists, philosophers of physics, researchers and advanced students in this field.” (Michael M. Dediu, Mathematical Reviews, Decemeber, 2017)
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 Table of contents (12 chapters)


Classical physics on a finite phase space
Pages 2338

Quantum mechanics on a finitedimensional Hilbert space
Pages 3981

Classical physics on a general phase space
Pages 83101

Quantum physics on a general Hilbert space
Pages 103123

Symmetry in quantum mechanics
Pages 125188

Table of contents (12 chapters)
 Download Preface 1 PDF (74.9 KB)
 Download Sample pages 2 PDF (379.7 KB)
 Download Table of contents PDF (64.4 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Foundations of Quantum Theory
 Book Subtitle
 From Classical Concepts to Operator Algebras
 Authors

 Klaas Landsman
 Series Title
 Fundamental Theories of Physics
 Series Volume
 188
 Copyright
 2017
 Publisher
 Springer International Publishing
 Copyright Holder
 The Author(s)
 eBook ISBN
 9783319517773
 DOI
 10.1007/9783319517773
 Hardcover ISBN
 9783319517766
 Softcover ISBN
 9783319847382
 Series ISSN
 01681222
 Edition Number
 1
 Number of Pages
 XXXVI, 861
 Number of Illustrations
 1 b/w illustrations, 8 illustrations in colour
 Topics