Fundamental Theories of Physics
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Foundations of Quantum Theory

From Classical Concepts to Operator Algebras

Authors: Landsman, Klaas

  • 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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  • ISBN 978-3-319-51777-3
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover £44.99
price for United Kingdom (gross)
  • ISBN 978-3-319-51776-6
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  • Usually dispatched within 3 to 5 business days.
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.

About the authors

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.  

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Table of contents (12 chapters)

  • Classical physics on a finite phase space

    Landsman, Klaas

    Pages 23-38

  • Quantum mechanics on a finite-dimensional Hilbert space

    Landsman, Klaas

    Pages 39-81

  • Classical physics on a general phase space

    Landsman, Klaas

    Pages 83-101

  • Quantum physics on a general Hilbert space

    Landsman, Klaas

    Pages 103-123

  • Symmetry in quantum mechanics

    Landsman, Klaas

    Pages 125-188

Buy this book

eBook  
  • ISBN 978-3-319-51777-3
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover £44.99
price for United Kingdom (gross)
  • ISBN 978-3-319-51776-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Quantum Theory
Book Subtitle
From Classical Concepts to Operator Algebras
Authors
Series Title
Fundamental Theories of Physics
Series Volume
188
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-51777-3
DOI
10.1007/978-3-319-51777-3
Hardcover ISBN
978-3-319-51776-6
Series ISSN
0168-1222
Edition Number
1
Number of Pages
XXXVI, 861
Number of Illustrations and Tables
1 b/w illustrations, 8 illustrations in colour
Topics