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This book will be useful to anyone who wants to understand the use of quantum theory for the description of physical processes. It is a graduate level text, ideal for independent study, and includes numerous figures, exercises, bibliographical references, and even some computer programs.

The first chapters introduce formal tools: the mathematics are precise, but not excessively abstract. The physical interpretation too is rigorous. It makes no use of the uncertainty principle of other ill-defined notions. The central part of the book is devoted to Bell's theorem and to the Kochen-Specker theorem. It is here that quantum phenomena depart most radically from classical physics. There has recently been considerable progress on these issues, and the latest developments have been included. The final chapters discuss further topics of current research: spacetime symmetries, quantum thermodynamics and information theory, semiclassical methods, irreversibility, quantum chaos, and especially the measuring process. In particular, it is shown how modern techniques allow the extraction of more information from a physical system than traditional measurement methods.

For physicists, mathematicians and philosophers of science with an interest in the applications and foundations of quantum theory. The volume is suitable as a supplementary graduate textbook.

Preface
PART I: GATHERING THE TOOLS
Chapter 1: Introduction to Quantum Physics
l - 1 . The downfall of classical concepts
l - 2 . The rise of randomness
l - 3 . Polarized photons
l - 4 . Introducing the quantum language
l - 5 . What is a measurement?
l - 6 . Historical remarks
l - 7 . Bibliography
Chapter 2: Quantum Tests
2-1. What is a quantum system?
2-2. Repeatable tests
2-3. Maximal quantum tests
2-4. Consecutive tests
2-5. The principle of interference
2-6. Transition amplitudes
2-7. Appendix: Bayes’s rule of statistical inference
2-8. Bibliography
Chapter 3: Complex Vector Space
3-1. The superposition principle
3-2. Metric properties
3-3. Quantum expectation rule
3-4. Physical implementation
3-5. Determination of a quantum state
3-6. Measurements and observables
3-7. Further algebraic properties
3-8. Quantum mixtures 72
3-9. Appendix: Dirac’s notation 77
3-10. Bibliography 78
Chapter 4: Continuous Variables 79
4-1. Hilbert space 79
4-2. Linear operators 84
4-3. Commutators and uncertainty relations 89
4-4. Truncated Hilbert space 95
4-5. Spectral theory 99
4-6. Classification of spectra 103
4-7. Appendix: Generalized functions 106
4-8. Bibliography 112
PART II: CRYPTODETERMINISM AND QUANTUM INSEPARABILITY
Chapter 5: Composite Systems 115
5 - l . Quantum correlations 115
5-2. Incomplete tests and partial traces 121
5-3. The Schmidt decomposition 123
5-4. Indistinguishable particles 126
5-5. Parastatistics 131
5-6. Fock space 137
5-7. Second quantization 142
5-8. Bibliography 147
Chapter 6: Bell’s Theorem 148
6-1. The dilemma of Einstein, Podolsky, and Rosen 148
6-2. Cryptodeterminism 155
6-3. Bell’s inequalities 160
6-4. Some fundamental issues 167
6-5. Other quantum inequalities 173
6-6. Higher spins 179
6-7. Bibliography 185
Chapter 7: Contextuality 187
7-1. Nonlocality versus contextuality 187
7-2. Gleason’s theorem 190
7-3. The Kochen-Specker theorem 196
7-4. Experimental and logical aspects of contextuality 202
7-5. Appendix: Computer test for Kochen-Specker contradiction 209
7-6. Bibliography 211
Table of Contents
PART III: QUANTUM DYNAMICS AND INFORMATION
Chapter 8: Spacetime Symmetries
8-1. What is a symmetry?
8-2. Wigner’s theorem
8-3. Continuous transformations
8-4. The momentum operator
8-5. The Euclidean group
8-6. Quantum dynamics
8-7. Heisenberg and Dirac pictures
8-8. Galilean invariance
8-9. Relativistic invariance
8-10. Forms of relativistic dynamics
8-11. Space reflection and time reversal
8-12. Bibliography
Chapter 9: Information and Thermodynamics
9-1. Entropy
9-2. Thermodynamic equilibrium
9-3. Ideal quantum gas
9-4. Some impossible processes
9-5. Generalized quantum tests
9-6. Neumark’s theorem
9-7. The limits of objectivity
9-8. Quantum cryptography and teleportation
9-9. Bibliography
Chapter 10: Semiclassical Methods
10-1. The correspondence principle
10-2. Motion and distortion of wave packets
10-3. Classical action
10-4. Quantum mechanics in phase space
10-5. Koopman’s theorem
10-6. Compact spaces
10-7. Coherent states
10-8. Bibliography
Chapter 11: Chaos and Irreversibility
11-1. Discrete maps
11-2. Irreversibility in classical physics
11-3. Quantum aspects of classical chaos
11-4. Quantum maps
11-5. Chaotic quantum motion
11-6. Evolution of pure states into mixtures 369
11-7. Appendix: P OST SCRIPT code for a map 370
11-8. Bibliography 371
Chapter 12: The Measuring Process 3 7 3
12-1. The ambivalent observer 373
12-2. Classical measurement theory 378
12-3. Estimation of a static parameter 385
12-4. Time-dependent signals 387
12-5. Quantum Zeno effect 392
12-6. Measurements of finite duration 400
12-7. The measurement of time 405
12-8. Time and energy complementarity 413
12-9. Incompatible observables 417
12-10. Approximate reality 423
12-11. Bibliography 428
Author Index 430
Subject Index
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