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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