Ensembles on Configuration Space: Classical, Quantum, and Beyond

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Springer, Jun 11, 2016 - Science - 280 pages

This book describes a promising approach to problems in the foundations of quantum mechanics, including the measurement problem. The dynamics of ensembles on configuration space is shown here to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian. Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices and quantum matter fields interacting gravitationally with a classical spacetime.

 

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Contents

1 Introduction
3
2 Observables Symmetries and Constraints
19
3 Interaction Locality and Measurement
43
4 Thermodynamics and Mixtures on Configuration Space
61
Part II Axiomatic Approaches to Quantum Mechanics
84
5 Quantization of Classical Ensembles via an Exact Uncertainty Principle
85
6 The Geometry of Ensembles on Configuration Space
115
7 Local Representations of Rotations on Discrete Configuration Spaces
141
8 Hybrid QuantumClassical Ensembles
161
9 Consistency of Hybrid QuantumClassical Ensembles
191
Part IV Classical Gravitational Fields and Their Interaction with Quantum Fields
221
10 Ensembles of Classical Gravitational Fields
223
11 Coupling of Quantum Fields to Classical Gravity
243
Appendix AVariational Derivatives and Integrals
273
Index
277
Copyright

Part III Hybrid QuantumClassical Systems
160

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About the author (2016)

Michael Hall works at the Centre for Quantum Dynamics at Griffith University in Brisbane, Australia. His research covers many areas of the foundations of quantum mechanics, including quantum information theory, quantum metrology, uncertainty relations, quantum time observables and interpretational aspects.

Marcel Reginatto is a physicist at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, Germany. His research in theoretical physics focuses on foundations of physics, with emphasis on quantum theory and general relativity. His work in applied physics concerns analysis of data and mathematical models of experiments.

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