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Ensembles on Configuration Space: Classical, Quantum, and Beyond

โœ Scribed by Michael J. W. Hall, Marcel Reginatto


Publisher
Springer
Year
2016
Tongue
English
Leaves
284
Series
Fundamental Theories of Physics 184
Edition
1st ed.
Category
Library

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โœฆ Synopsis


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.ย  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.

โœฆ Table of Contents


Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Introduction....Pages 3-17
Observables, Symmetries and Constraints....Pages 19-42
Interaction, Locality and Measurement....Pages 43-59
Thermodynamics and Mixtures on Configuration Space....Pages 61-81
Front Matter....Pages 83-83
Quantization of Classical Ensembles via an Exact Uncertainty Principle....Pages 85-113
The Geometry of Ensembles on Configuration Space....Pages 115-139
Local Representations of Rotations on Discrete Configuration Spaces....Pages 141-157
Front Matter....Pages 159-159
Hybrid Quantum-Classical Ensembles....Pages 161-190
Consistency of Hybrid Quantum-Classical Ensembles....Pages 191-220
Front Matter....Pages 221-221
Ensembles of Classical Gravitational Fields....Pages 223-242
Coupling of Quantum Fields to Classical Gravity....Pages 243-272
Back Matter....Pages 273-280

โœฆ Subjects


Physics;Mathematical physics;Quantum physics;Statistical physics;Dynamical systems;Quantum Physics;Mathematical Physics;Statistical Physics, Dynamical Systems and Complexity


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