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Ensembles on Configuration Space

Classical, Quantum, and Beyond

  • Michael J. W. Hall
  • Marcel Reginatto

Part of the Fundamental Theories of Physics book series (FTPH, volume 184)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. General Properties of Ensembles on Configuration Space

    1. Front Matter
      Pages 1-1
    2. Michael J. W. Hall, Marcel Reginatto
      Pages 3-17
    3. Michael J. W. Hall, Marcel Reginatto
      Pages 19-42
    4. Michael J. W. Hall, Marcel Reginatto
      Pages 43-59
    5. Michael J. W. Hall, Marcel Reginatto
      Pages 61-81
  3. Axiomatic Approaches to Quantum Mechanics

    1. Front Matter
      Pages 83-83
    2. Michael J. W. Hall, Marcel Reginatto
      Pages 85-113
    3. Michael J. W. Hall, Marcel Reginatto
      Pages 115-139
    4. Michael J. W. Hall, Marcel Reginatto
      Pages 141-157
  4. Hybrid Classical-Quantum Systems

    1. Front Matter
      Pages 159-159
    2. Michael J. W. Hall, Marcel Reginatto
      Pages 161-190
    3. Michael J. W. Hall, Marcel Reginatto
      Pages 191-220
  5. Classical Gravitational Fields and Their Interaction with Quantum Fields

    1. Front Matter
      Pages 221-221
    2. Michael J. W. Hall, Marcel Reginatto
      Pages 223-242
    3. Michael J. W. Hall, Marcel Reginatto
      Pages 243-272
  6. Back Matter
    Pages 273-280

About this book

Introduction

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.

Keywords

Axiomatic Quantum Mechanics Dynamics on Configuration Space Fisher Information Metric Quantum Measurement Problem and Decoherence Statistical Mechanics on Configuration Space Unified Description of Quantum and Classical Mechanics

Authors and affiliations

  • Michael J. W. Hall
    • 1
  • Marcel Reginatto
    • 2
  1. 1.Centre for Quantum DynamicsGriffith University Centre for Quantum DynamicsBrisbaneAustralia
  2. 2.Physikalisch-Technische BundesanstaltBraunschweigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-34166-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-34164-4
  • Online ISBN 978-3-319-34166-8
  • Series Print ISSN 0168-1222
  • Series Online ISSN 2365-6425
  • Buy this book on publisher's site
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