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Hall M.J.W., Reginatto M. Ensembles on Configuration Space: Classical, Quantum, and Beyond

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Hall M.J.W., Reginatto M. Ensembles on Configuration Space: Classical, Quantum, and Beyond
Springer International Publishing, Switzerland, 2016. – 284. – ISBN-10: 3319341642
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 space time.
Quantum Physics
Mathematical Physics
Statistical Physics, Dynamical Systems and Complexity
General Properties of Ensembles on Configuration Space
Observables, Symmetries and Constraints
Interaction, Locality and Measurement
Thermodynamics and Mixtures on Configuration Space
Axiomatic Approaches to Quantum Mechanics
Quantization of Classical Ensembles via an Exact Uncertainty Principle
The Geometry of Ensembles on Configuration Space
Local Representations of Rotations on Discrete Configuration Spaces
Hybrid Quantum-Classical Systems
Hybrid Quantum-Classical Ensembles
Consistency of Hybrid Quantum-Classical Ensembles
Classical Gravitational Fields and Their Interaction with Quantum Fields
Ensembles of Classical Gravitational Fields
Coupling of Quantum Fields to Classical Gravity
Appendix A: Variational Derivatives and Integrals
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