04029 am 22007333u 450 991022000750332120230405173255.03-319-51777-510.1007/978-3-319-51777-3(CKB)4340000000061852(DE-He213)978-3-319-51777-3(MiAaPQ)EBC5595255(Au-PeEL)EBL5595255(OCoLC)1076259096(oapen)https://directory.doabooks.org/handle/20.500.12854/58238(PPN)201471647(EXLCZ)99434000000006185220170512d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierFoundations of Quantum Theory From Classical Concepts to Operator Algebras /by Klaas Landsman1st ed. 2017.Springer NatureCham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XXXVI, 861 p. 9 illus., 8 illus. in color.)Fundamental Theories of Physics,0168-1222 ;1883-319-51776-7 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.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.Fundamental Theories of Physics,0168-1222 ;188Quantum physicsMathematical physicsPhysicsMatrix theoryAlgebraQuantum PhysicsMathematical PhysicsHistory and Philosophical Foundations of PhysicsLinear and Multilinear Algebras, Matrix TheoryAlgebraMatrix theoryQuantum physicsMathematical physicsQuantum physics.Mathematical physics.Physics.Matrix theory.Algebra.Quantum Physics.Mathematical Physics.History and Philosophical Foundations of Physics.Linear and Multilinear Algebras, Matrix Theory.530.12Landsman Klaasauthttp://id.loc.gov/vocabulary/relators/aut821832MiAaPQMiAaPQMiAaPQBOOK9910220007503321Foundations of Quantum Theory2119925UNINA