## Decoherence and the Appearance of a Classical World in Quantum TheoryWhen we were preparing the first edition of this book, the concept of de coherence was known only to a minority of physicists. In the meantime, a wealth of contributions has appeared in the literature - important ones as well as serious misunderstandings. The phenomenon itself is now experimen tally clearly established and theoretically well understood in principle. New fields of application, discussed in the revised book, are chaos theory, informa tion theory, quantum computers, neuroscience, primordial cosmology, some aspects of black holes and strings, and others. While the first edition arose from regular discussions between the authors, thus leading to a clear" entanglement" of their otherwise quite different chap ters, the latter have thereafter evolved more or less independently. While this may broaden the book's scope as far as applications and methods are con cerned, it may also appear confusing to the reader wherever basic assumptions and intentions differ (as they do). For this reason we have rearranged the or der of the authors: they now appear in the same order as the chapters, such that those most closely related to the "early" and most ambitious concept of decoherence are listed first. The first three authors (Joos, Zeh, Kiefer) agree with one another that decoherence (in contradistinction to the Copen hagen interpretation) allows one to eliminate primary classical concepts, thus neither relying on an axiomatic concept of observables nor on a probability interpretation of the wave function in terms of classical concepts. |

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### Contents

Introduction | 1 |

Basic Concepts and Their Interpretation | 7 |

212 Superselection Rules | 11 |

213 Decoherence by Measurements | 13 |

22 Observables as a Derived Concept | 17 |

23 The Measurement Problem | 21 |

24 Density Matrix Coarse Graining and Events | 33 |

25 Conclusions | 40 |

611 Spaces of States | 262 |

612 Spaces of Observables | 267 |

613 Superselection Rules | 275 |

62 Symmetries and Superselection Rules | 278 |

621 Symmetries | 279 |

622 Superselection Rules from Symmetries | 284 |

The Univalence Superselection Rule | 285 |

624 Discussion and Caveats | 287 |

Decoherence Through Interaction with the Environment | 41 |

31 The General Mechanisms of Decoherence | 47 |

312 Scattering Processes | 55 |

313 EnvironmentInduced Superselection Rules | 57 |

32 Localization of Objects | 62 |

321 Localization Through Ideal Measurements | 64 |

3212 Equation of Motion | 70 |

3213 Decohering Wave Packets | 75 |

3214 More General RecoilFree Decoherence | 78 |

322 Decoherence and Dissipation | 79 |

3222 Ehrenfest Theorems | 87 |

3223 Decoherence Versus Friction | 89 |

323 Wigner Function Description of Decoherence | 90 |

324 Molecular Structure | 99 |

325 Decoherence in the Brain | 107 |

33 Dynamical Consequences | 109 |

331 The Quantum Zeno Effect | 110 |

3311 Phenomenological Description | 111 |

3312 An Experimental Test | 118 |

3313 Models for the Quantum Zeno Effect | 122 |

332 Master Equations | 126 |

3322 Lindblads Form of Master Equations | 133 |

333 Dynamical Stability of States | 135 |

3331 Sensitivity to the Presence of an Environment | 136 |

3332 Decoherence and Quantum Computation | 145 |

3333 Quantum Nondemolition Measurements | 147 |

334 Decoherence and Quantum Chaos | 149 |

3342 Example | 152 |

3343 Quantum ? Chaos in the Solar System | 156 |

3344 Decoherence Through Chaotic Environments | 159 |

34 Interpretational Issues | 161 |

342 Quantum Information and Teleportation | 172 |

343 True False and Fake Decoherence | 175 |

Decoherence in Quantum Field Theory and Quantum Gravity | 181 |

41 Decoherence in Quantum Electrodynamics | 182 |

412 Measurement of Electromagnetic Fields by Charges | 188 |

42 Decoherence and the Gravitational Field | 192 |

422 The Formalism of Quantum Cosmology | 196 |

423 Decoherence in Quantum Cosmology | 199 |

424 Classicality of Primordial Fluctuations in the Early Universe | 209 |

425 Black Holes Wormholes and String Theory | 218 |

Consistent Histories and Decoherence | 227 |

51 Influence Functional and Its Application to Quantum Brownian Motion | 229 |

52 Definition and Properties of Consistent Histories | 238 |

53 Reduced Density Matrix and Decoherence | 247 |

54 Consistent Histories Arrow of Time and Quantum Gravity | 251 |

Superselection Rules and Symmetries | 259 |

61 States Observables and Superselection Rules | 261 |

63 Physical Symmetries Versus Gauge Transformations | 289 |

632 Symmetries and Redundant State Spaces | 292 |

633 Symmetries Redundancies and Superselection Rules | 297 |

64 Superselection Rules in Field Theory | 303 |

641 Charge and Asymptotic FluxDistribution in QED | 304 |

642 Poincare Charges in General Relativity | 310 |

643 Decoherence and Charge Superselection Rules | 312 |

Open Quantum Systems | 317 |

71 Reduced Dynamics | 319 |

72 Projection Methods | 321 |

73 Generalized Master Equations | 327 |

74 Markov Approximation and Semigroups | 330 |

75 Quantum Stochastic Processes | 333 |

76 Induced Superselection Sectors | 339 |

762 Hamiltonian Models of Decoherence | 341 |

7621 The ArakiZurek Models | 343 |

7622 Particle Coupled to a Massless Boson Field | 345 |

7623 Models with Scattering | 347 |

7624 Heisenberg Picture | 348 |

77 Mathematical Supplement | 350 |

772 Complete Positivity | 354 |

773 Entropy Inequalities | 355 |

Stochastic Collapse Models | 357 |

812 Decoherence Collapse Measurement | 358 |

813 Various Approaches to Collapse | 363 |

82 Spontaneous Collapse Models | 369 |

822 Spontaneous Localization by a Jump Process | 370 |

823 Continuous Spontaneous Localization | 373 |

83 Spontaneous Localization Quantum State Diffusion and Decoherence | 378 |

Related Concepts and Methods | 383 |

92 Ergodicity and Irreversible Amplification | 385 |

93 Dressing of States | 387 |

94 Symmetry Breaking and Collective Motion | 388 |

A1 Equation of Motion of a Mass Point | 395 |

A2 Solutions for the Equation of Motion | 399 |

A22 Green Functions | 402 |

A23 Some Derived Quantities | 403 |

A3 Elementary Properties of Composite Systems in Quantum Mechanics | 407 |

A4 Quantum Correlations | 415 |

A5 Hamiltonian Formulation of Quantum Mechanics | 419 |

A6 Galilean Symmetry of NonRelativistic Quantum Mechanics | 425 |

A7 Stochastic Processes | 433 |

A72 Markov Chains | 434 |

A73 Stochastic Processes | 436 |

A74 The FokkerPlanck Equation | 437 |

A75 Stochastic Differential Equations | 439 |

References | 445 |

### Other editions - View all

Decoherence and the Appearance of a Classical World in Quantum Theory Domenico Giulini,Erich Joos,Claus Kiefer No preview available - 2014 |

### Common terms and phrases

algebra approximation assumed atom Brownian motion Chap classical coherence commute components concept condition consider consistent histories corresponding coupling decay decohered decoherence decoherence functional defined degrees of freedom denotes density matrix depends derived described discussed distribution dynamics eigenstates energy ensemble entanglement entropy environment environmental decoherence equation of motion evolution example factor field finite formal Ghirardi given gravitational Hamiltonian Heisenberg picture Hence Hilbert space initial interaction interpretation Kiefer leads linear macroscopic master equation measurement molecules momentum Neumann observables oscillator parameter particle phase space photon Phys physical pointer position probability projection operators projectors properties pure quantum mechanics quantum theory quantum Zeno effect reduced density matrix representation represented result rotation scattering Schrodinger equation Sect spatial statistical operator stochastic process subspaces subsystem superposition superposition principle superselection rules superselection sectors theorem tion transition unitary variables vector wave function wave packets Wigner function Zeno effect Zurek