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Format: 1 electronic resource (394 pages)

Content: This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.

Note: English

Additional Edition: ISBN 90-831789-2-7

Language: English

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Format: 1 Online-Ressource (XXXVI, 861 p. 9 illus., 8 illus. in color).

ISBN: 978-3-319-51777-3

Series Statement: Fundamental Theories of Physics volume 188

Note: Open Access-Titel

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-51776-6

Language: English

Subjects: Physics

Keywords: Quantentheorie ; Mathematische Physik ; Quantenmechanik

DOI: 10.1007/978-3-319-51777-3

URL: Volltext  (kostenfrei)

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

Edition: 1st ed. 2017.

ISBN: 3-319-51777-5

Series Statement: Fundamental Theories of Physics, 188

Content: 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.

Note: 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. , English

Additional Edition: ISBN 3-319-51776-7

Language: English

DOI: 10.1007/978-3-319-51777-3

UID:

Format: XXXVI, 861 p. 9 illus., 8 illus. in color. , online resource.

ISBN: 9783319517773

Series Statement: Fundamental Theories of Physics, 188

Content: 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.

Note: 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.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783319517766

Language: English

DOI: 10.1007/978-3-319-51777-3

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Format: 1 Online-Ressource (861 p.)

ISBN: 9783319517773

Series Statement: Fundamental Theories of Physics

Content: Quantum physics; Mathematical physics; Matrix theory; Algebra

Note: English

Language: English

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Format: XII, 355 S. , 24 cm

ISBN: 9783764366087 , 3764366087

Series Statement: Progress in mathematics 198

Note: Includes bibliographical references

Language: English

Subjects: Physics , Mathematics

Keywords: Symplektische Mannigfaltigkeit ; Geometrische Quantisierung ; Konferenzschrift

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URL: http://www.loc.gov/catdir/enhancements/fy0812/2001043134-d.html

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Format: 1 Online-Ressource (276 p.)

ISBN: 9783319263007 , 9783319146935

Series Statement: The Frontiers Collection

Content: Human Genetics; Philosophy of Science; Probability Theory

Note: English

Language: English

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Format: 1 Online-Ressource (XII, 355 p)

ISBN: 9783034883641 , 9783034895354

Series Statement: Progress in Mathematics 198

Note: The purpose of this volume is to present new techniques and ideas that have a di­ rect significance for the description of stratified (symplectic) spaces and their quan­ tization. The book grew out of a Research-in-Pairs Workshop held at Oberwolfach from 2-6 August, 1999, organized by the editors with Martin Bordemann. They are grateful to the Volkswagen-Stiftung and to the Mathematisches Forschungszen­ trum Oberwolfach, particularly to its director, Matthias Kreck, for financial and other support. The papers by Cattaneo and Felder, Huebschmann, Landsman, Pflaum, Schli­ chenmaier, Schomerus, Schroers, and Sengupta are based on talks given at the workshop. To obtain a more complete picture of the field, the editors invited a number of outside contributions as well. Thus they are happy to include the papers by Benameur and Nistor, Braverman, Fedosov, and Lauter and Nistor. All papers were refereed. The opening article by Marsden and Weinstein provides a historical and personal overview of the subject. In the bulk of the book the reader may identify two fundamentally different approaches. The first associates a commutative algebra of functions to a singular space, preferably also equipped with a Poisson bracket, which one may subse­ quently try to quantize. This generically involves techniques from algebraic and differential geometry. Here the papers by Braverman, Cattaneo and Felder, Pflaum, and Schlichenmaier are of a general nature, whereas Huebschmann, Schomerus, Schroers, and Sengupta are specifically concerned with the moduli spaces M. (Cf

Language: English

Keywords: Symplektische Mannigfaltigkeit ; Geometrische Quantisierung ; Konferenzschrift

DOI: 10.1007/978-3-0348-8364-1

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Author information: Pflaum, Markus J. 1965-

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Format: XIX, 529 S. , graph. Darst. , 24 cm

ISBN: 9781461272427 , 9780387983189 , 038798318X

Series Statement: Springer monographs in mathematics

Note: Literaturverz. S. [483] - 520

Additional Edition: ISBN 9781461216803

Language: English

Subjects: Physics , Mathematics

Keywords: Quantenmechanik ; Mathematische Methode ; Quantenfeldtheorie ; Mathematische Methode ; Mathematische Physik ; Quantenmechanik ; Mathematische Methode ; Quantenfeldtheorie ; Mathematische Methode ; Mathematische Physik

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URL: http://dx.doi.org/10.1007/978-1-4612-1680-3

URL: http://www.loc.gov/catdir/enhancements/fy0818/98018391-d.html

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Format: 1 online resource (881 pages)

Edition: 1st ed.

ISBN: 9783319517773

Series Statement: Fundamental Theories of Physics Series ; v.188

Note: Intro -- Preface -- Contents -- Introduction -- Part I C0(X) and B(H) -- 1 Classical physics on a finite phase space -- 1.1 Basic constructions of probability theory -- 1.2 Classical observables and states -- 1.3 Pure states and transition probabilities -- 1.4 The logic of classical mechanics -- 1.5 The GNS-construction for C(X) -- Notes -- 2 Quantum mechanics on a finite-dimensional Hilbert space -- 2.1 Quantum probability theory and the Born rule -- 2.2 Quantum observables and states -- 2.3 Pure states in quantum mechanics -- 2.4 The GNS-construction for matrices -- 2.5 The Born rule from Bohrification -- 2.6 The Kadison-Singer Problem -- 2.7 Gleason's Theorem -- 2.8 Proof of Gleason's Theorem -- 2.9 Effects and Busch's Theorem -- 2.10 The quantum logic of Birkhoff and von Neumann -- Notes -- 3 Classical physics on a general phase space -- 3.1 Vector fields and their flows -- 3.2 Poisson brackets and Hamiltonian vector fields -- 3.3 Symmetries of Poisson manifolds -- 3.4 The momentum map -- Notes -- 4 Quantum physics on a general Hilbert space -- 4.1 The Born rule from Bohrification (II) -- 4.2 Density operators and normal states -- 4.3 The Kadison-Singer Conjecture -- 4.4 Gleason's Theorem in arbitrary dimension -- Notes -- 5 Symmetry in quantum mechanics -- 5.1 Six basic mathematical structures of quantum mechanics -- 5.2 The case -- 5.3 Equivalence between the six symmetry theorems -- 5.4 Proof of Jordan's Theorem -- 5.5 Proof of Wigner's Theorem -- 5.6 Some abstract representation theory -- 5.7 Representations of Lie groups and Lie algebras -- 5.8 Irreducible representations of -- 5.9 Irreducible representations of compact Lie groups -- 5.10 Symmetry groups and projective representations -- 5.11 Position, momentum, and free Hamiltonian -- 5.12 Stone's Theorem -- Notes -- Part II Between C0(X) and B(H). , 6 Classical models of quantum mechanics -- 6.1 From von Neumann to Kochen-Specker -- 6.2 The Free Will Theorem -- 6.3 Philosophical intermezzo: Free will in the Free Will Theorem -- 6.4 Technical intermezzo: The GHZ-Theorem -- 6.5 Bell's theorems -- 6.6 The Colbeck-Renner Theorem -- Notes -- 7 Limits: Small h̄ -- 7.1 Deformation quantization -- 7.2 Quantization and internal symmetry -- 7.3 Quantization and external symmetry -- 7.4 Intermezzo: The Big Picture -- 7.5 Induced representations and the imprimitivity theorem -- 7.6 Representations of semi-direct products -- 7.7 Quantization and permutation symmetry -- Notes -- 8 Limits: large N -- 8.1 Large quantum numbers -- 8.2 Large systems -- 8.3 Quantum de Finetti Theorem -- 8.4 Frequency interpretation of probability and Born rule -- 8.5 Quantum spin systems: Quasi-local C*-algebras -- 8.6 Quantum spin systems: Bundles of C*-algebras -- Notes -- 9 Symmetry in algebraic quantum theory -- 9.1 Symmetries of C*-algebras and Hamhalter's Theorem -- 9.2 Unitary implementability of symmetries -- 9.3 Motion in space and in time -- 9.4 Ground states of quantum systems -- 9.5 Ground states and equilibrium states of classical spin systems -- 9.6 Equilibrium (KMS) states of quantum systems -- Notes -- 10 Spontaneous Symmetry Breaking -- 10.1 Spontaneous symmetry breaking: The double well -- 10.2 Spontaneous symmetry breaking: The flea -- 10.3 Spontaneous symmetry breaking in quantum spin systems -- 10.4 Spontaneous symmetry breaking for short-range forces -- 10.5 Ground state(s) of the quantum Ising chain -- 10.6 Exact solution of the quantum Ising chain: -- 10.7 Exact solution of the quantum Ising chain: -- 10.8 Spontaneous symmetry breaking in mean-field theories -- 10.9 The Goldstone Theorem -- 10.10 The Higgs mechanism -- Notes -- 11 The measurement problem -- 11.1 The rise of orthodoxy. , 11.2 The rise of modernity: Swiss approach and Decoherence -- 11.3 Insolubility theorems -- 11.4 The Flea on Schrödinger's Cat -- Notes -- 12 Topos theory and quantum logic -- 12.1 C*-algebras in a topos -- 12.2 The Gelfand spectrum in constructive mathematics -- 12.3 Internal Gelfand spectrum and intuitionistic quantum logic -- 12.4 Internal Gelfand spectrum for arbitrary C*-algebras -- 12.5 "Daseinisation" and Kochen-Specker Theorem -- Notes -- Appendix A Finite-dimensional Hilbert spaces -- A.1 Basic definitions -- A.2 Functionals and the adjoint -- A.3 Projections -- A.4 Spectral theory -- A.5 Positive operators and the trace -- Notes -- Appendix B Basic functional analysis -- B.1 Completeness -- B.2 lp spaces -- B.3 Banach spaces of continuous functions -- B.4 Basic measure theory -- B.5 Measure theory on locally compact Hausdorff spaces -- B.6 Lp spaces -- B.7 Morphisms and isomorphisms of Banach spaces -- B.8 The Hahn-Banach Theorem -- B.9 Duality -- B.10 The Krein-Milman Theorem -- B.11 Choquet's Theorem -- B.12 A précis of infinite-dimensional Hilbert space -- B.13 Operators on infinite-dimensional Hilbert space -- B.14 Basic spectral theory -- B.15 The spectral theorem -- B.16 Abelian ∗-algebras in B(H) -- B.17 Classification of maximal abelian ∗-algebras in B(H) -- B.18 Compact operators -- B.19 Spectral theory for self-adjoint compact operators -- B.20 The trace -- B.21 Spectral theory for unbounded self-adjoint operators -- Notes -- Appendix C Operator algebras -- C.1 Basic definitions and examples -- C.2 Gelfand isomorphism -- C.3 Gelfand duality -- C.4 Gelfand isomorphism and spectral theory -- C.5 C*-algebras without unit: general theory -- C.6 C*-algebras without unit: commutative case -- C.7 Positivity in C*-algebras -- C.8 Ideals in Banach algebras -- C.9 Ideals in C*-algebras -- C.10 Hilbert C*-modules and multiplier algebras. , C.11 Gelfand topology as a frame -- C.12 The structure of C*-algebras -- C.13 Tensor products of Hilbert spaces and C*-algebras -- C.14 Inductive limits and infinite tensor products of C*-algebras -- C.15 Gelfand isomorphism and Fourier theory -- C.16 Intermezzo: Lie groupoids -- C.17 C*-algebras associated to Lie groupoids -- C.18 Group C*-algebras and crossed product algebras -- C.19 Continuous bundles of C*-algebras -- C.20 von Neumann algebras and the σ-weak topology -- C.21 Projections in von Neumann algebras -- C.22 The Murray-von Neumann classification of factors -- C.23 Classification of hyperfinite factors -- C.24 Other special classes of C*-algebras -- C.25 Jordan algebras and (pure) state spaces of C*-algebras -- Notes -- Appendix D Lattices and logic -- D.1 Order theory and lattices -- D.2 Propositional logic -- D.3 Intuitionistic propositional logic -- D.4 First-order (predicate) logic -- D.5 Arithmetic and set theory -- Notes -- Appendix E Category theory and topos theory -- E.1 Basic definitions -- E.2 Toposes and functor categories -- E.3 Subobjects and Heyting algebras in a topos -- E.4 Internal frames and locales in sheaf toposes -- E.5 Internal language of a topos -- Notes -- References -- Index.

Additional Edition: Print version: Landsman, Klaas Foundations of Quantum Theory Cham : Springer International Publishing AG,c2017 ISBN 9783319517766

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