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  • Book
  • Open Access
  • © 2017

Foundations of Quantum Theory

From Classical Concepts to Operator Algebras


  • 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

  • Includes supplementary material:

Part of the book series: Fundamental Theories of Physics (FTPH, volume 188)

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Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxxvi
  2. C0(X) and B(H)

    1. Front Matter

      Pages 21-21
    2. Classical physics on a finite phase space

      • Klaas Landsman
      Pages 23-38Open Access
    3. Quantum mechanics on a finite-dimensional Hilbert space

      • Klaas Landsman
      Pages 39-81Open Access
    4. Classical physics on a general phase space

      • Klaas Landsman
      Pages 83-101Open Access
    5. Quantum physics on a general Hilbert space

      • Klaas Landsman
      Pages 103-123Open Access
    6. Symmetry in quantum mechanics

      • Klaas Landsman
      Pages 125-188Open Access
  3. Between C0(X) and B(H)

    1. Front Matter

      Pages 189-189
    2. Classical models of quantum mechanics

      • Klaas Landsman
      Pages 191-245Open Access
    3. Limits: Small \(\hbar \)

      • Klaas Landsman
      Pages 247-291Open Access
    4. Limits: large N

      • Klaas Landsman
      Pages 293-331Open Access
    5. Symmetry in algebraic quantum theory

      • Klaas Landsman
      Pages 333-366Open Access
    6. Spontaneous Symmetry Breaking

      • Klaas Landsman
      Pages 367-433Open Access
    7. The measurement problem

      • Klaas Landsman
      Pages 435-457Open Access
    8. Topos theory and quantum logic

      • Klaas Landsman
      Pages 459-494Open Access
  4. Back Matter

    Pages 495-881

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 Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer 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. 


  • Quantum measurement problem
  • Spontaneous symmetry breaking
  • Open Access
  • von Neumann operator algebras
  • C*-algebras
  • Quantum mechanics and topos theory
  • Formalized Copenhagen Interpretation
  • Born rule
  • Bohrification
  • matrix theory


“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 classical-quantum 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)

Authors and Affiliations

  • IMAPP, Radboud University Nijmegen IMAPP, Nijmegen, The Netherlands

    Klaas Landsman

About the author

Klaas Landsman (1963) obtained his PhD in Theoretical High-Energy Physics from the University of Amsterdam in 1989. He was a research fellow at the University of Cambridge from 1989-1997, with a sojourn as Alexander von Humboldt Fellow in Hamburg from 1993-94. He was subsequently a Royal Academy Research Fellow at the University of Amsterdam from 1997-2002, 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 non-commutative geometry and with the mathematical foundations of quantum theory.   

Bibliographic Information

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)