1.

Record Nr.

UNINA9910220007503321

Autore

Landsman Klaas

Titolo

Foundations of Quantum Theory : From Classical Concepts to Operator Algebras / / by Klaas Landsman

Pubbl/distr/stampa

Springer Nature

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

ISBN

3-319-51777-5

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (XXXVI, 861 p. 9 illus., 8 illus. in color.)

Collana

Fundamental Theories of Physics, , 0168-1222 ; ; 188

Disciplina

530.12

Soggetti

Quantum physics

Mathematical physics

Physics

Matrix theory

Algebra

Quantum Physics

Mathematical Physics

History and Philosophical Foundations of Physics

Linear and Multilinear Algebras, Matrix Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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.