Foundations of Quantum Theory: From Classical Concepts to Operator Algebras

Voorkant
Springer, 11 mei 2017 - 861 pagina's
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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.

 

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Inhoudsopgave

Introduction
1
Part I C0X and BH
21
1 Classical physics on a finite phase space
22
2 Quantum mechanics on a finitedimensional Hilbert space
39
3 Classical physics on a general phase space
83
4 Quantum physics on a general Hilbert space
102
5 Symmetry in quantum mechanics
125
Part II Between C0X and BH
189
10 Spontaneous Symmetry Breaking
367
11 The measurement problem
434
12 Topos theory and quantum logic
459
Appendix A Finitedimensional Hilbert spaces
495
Appendix B Basic functional analysis
514
Appendix C Operator algebras
645
Appendix D Lattices and logic
776
Appendix E Category theory and topos theory
805

6 Classical models of quantum mechanics
190
Small ̄h
247
large N
292
9 Symmetry in algebraic quantum theory
333

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Over de auteur (2017)

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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