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Foundations of Quantum Theory

  • Couverture cartonnée
  • 900 Nombre de pages
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This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Cope... Lire la suite
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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.

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


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.   

Introduction.- Part I Co(X) and B(H): Classical physics on a finite phase space.- Quantum mechanics on a finite-dimensional Hilbert space.- Classical physics on a general phase space.- Quantum physics on a general Hilbert space.- Symmetry in quantum mechanics.- Part II Between Co(X) and B(H): Classical models of quantum mechanics.- Limits: Small hbar.- Limits: large N.- Symmetry in algebraic quantum theory.- Spontaneous Symmetry Breaking.- The Measurement Problem.- Topos theory and quantum logic.- Appendix A: Finite-dimensional Hilbert spaces.- Appendix B: Basic functional analysis.- Appendix C: Operator algebras.- Appendix D: Lattices and logic.- Appendix E: Category theory and topos theory.- References.

Informations sur le produit

Titre: Foundations of Quantum Theory
Code EAN: 9783319847382
ISBN: 3319847384
Format: Couverture cartonnée
Editeur: Springer International Publishing
nombre de pages: 900
Poids: 1334g
Taille: H235mm x B155mm x T47mm
Année: 2018
Auflage: Softcover reprint of the original 1st ed. 2017