foreworded by Giorgio Parisi & by Gennaro Auletta (University “La Sapienza” (Roma I), Italy)

The aim of this book is twofold: to provide a comprehensive account of the foundations of the theory and to outline a theoretical and philosophical interpretation suggested from the results of the last twenty years.

There is a need to provide an account of the foundations of the theory because recent experience has largely confirmed the theory and offered a wealth of new discoveries and possibilities. On the other side, the following results have generated a new basis for discussing the problem of the interpretation: the new developments in measurement theory; the experimental generation of “Schrödinger cats”; recent developments which allow, for the first time, the simultaneous measurement of complementary observables; quantum information processing, teleportation and computation.

To accomplish this task, the book combines historical, systematic and thematic approaches.

• Basic Formalism and Extensions of Quantum Mechanics:
  • Where the Problems Begin
  • Basic Quantum Mechanics
  • Relativistic Quantum Mechanics
  • Quantum Optics
• The Copenhagen Interpretation:
  • First Interpretations of Quantum Mechanics
  • Uncertainty Principle
  • The Complementarity Principle
• First Foundations of Quantum Mechanics:
  • QM Axiomatics
  • Hilbert Spaces and Operators
  • Classical and Quantum Probability: An Overview
  • Geometric Phase
• Measurement Problem:
  • Some Preliminary Notions
  • Von Neumann Theory and Its Refinements
  • Many-World Interpretation
  • Solutions Using Classical or Semiclassical Apparata
  • Decoherence
  • Operational Stochastic QM
  • Non-Demolition Measurement Theory
  • Information Without Interaction
• Microphysics/Macrophysics:
  • Decoherence and Thermodynamics
  • Quantum Jumps
  • Reductions to Classical Case
  • Generation of the Cat
• Time and QM:
  • Consistent and Decohering Histories
  • Delayed Choice
  • Reversibility and Irreversibility
• Wave/Particle Dualism:
  • The Reality of Quantum Waves and States
  • The Indeterminacy of Quantum Waves and States
  • Between Wave and Particle
• Completeness and Determinism:
  • Einstein/Podolsky/Rosen Argument
  • Examination and Interpretation of Hidden-Variable Theories
  • Stochastic Generalization
• The Problem of Non-Locality:
  • Initial Criticisms of the Einstein/Podolsky/Rosen Argument
  • Bell Inequalities
  • The Problem of Separability as Such
  • More Exact Bounds for the Inequalities
  • Entanglement with Pure States and with Mixtures
  • Generalized Bell Inequalities
  • Bell Inequalities for Other Observables
  • Other Non-Local Effects
• Information and Quantum Mechanics:
  • Information and Entropy in Quantum Mechanics
  • Quantum Cryptography and Teleportation
  • Quantum Information and Computation
• Conclusions:
  • A Foundational Synthesis
  • Outline of an Interpretation of Quantum Mechanics