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Foundations of Quantum Gravity

Book Description

Exploring how the subtleties of quantum coherence can be consistently incorporated into Einstein's theory of gravitation, this book is ideal for researchers interested in the foundations of relativity and quantum physics. The book examines those properties of coherent gravitating systems that are most closely connected to experimental observations. Examples of consistent co-gravitating quantum systems whose overall effects upon the geometry are independent of the coherence state of each constituent are provided, and the properties of the trapping regions of non-singular black objects, black holes and a dynamic de Sitter cosmology are discussed analytically, numerically and diagrammatically. The extensive use of diagrams to summarise the results of the mathematics enables readers to bypass the need for a detailed understanding of the steps involved. Assuming some knowledge of quantum physics and relativity, the book provides text boxes featuring supplementary information for readers particularly interested in the philosophy and foundations of the physics.

Table of Contents

  1. Cover Page
  2. Half Title
  3. Title Page
  4. Copyright
  5. Table of Contents
  6. Preface
  7. Notations and Conventions
  8. Introduction
  9. Part I Galilean and special relativity
    1. 1 Classical special relativity
      1. 1.1 Foundations of special relativity
      2. 1.2 General motions in special relativity
      3. 1.3 Canonical proper-time dynamics
      4. 1.4 Conformal space-time diagrams
    2. 2 Quantum mechanics, classical, and special relativity
      1. 2.1 Fundamentals of quantum mechanics
      2. 2.2 Quantum mechanics and statistics
      3. 2.3 Quantum mechanics and gravity
      4. 2.4 Thermal properties of acceleration
    3. 3 Microscopic formulations of particle interactions
      1. 3.1 Non-perturbative scattering theory
      2. 3.2 Faddeev formulation of scattering theory
      3. 3.3 Unitarity, Poincaré covariance, and cluster decomposability
      4. 3.4 Lagrangian dynamics
    4. 4 Group theory in quantum mechanics
      1. 4.1 Quantum mechanics and the Galilean group
      2. 4.2 Quantization conditions on gauge fields
      3. 4.3 Quantum mechanics and special relativity
      4. 4.4 Particles and the Poincaré group
  10. Part II General relativity
    1. 5 Fundamentals of general relativity
      1. 5.1 From special to general relativity
      2. 5.2 Einstein’s equations
      3. 5.3 Time-independent spherically symmetric solutions
      4. 5.4 An axially stationary rotating geometry
    2. 6 Quantum mechanics in curved space-time backgrounds
      1. 6.1 Quantum coherence and gravity
      2. 6.2 Lagrangian dynamics of quantum systems
      3. 6.3 Self-gravitation
    3. 7 The physics of horizons and trapping regions
      1. 7.1 Static horizons in Rindler, Schwarzschild, and radially stationary geometries
      2. 7.2 Dynamic spherically symmetric black holes
      3. 7.3 Macroscopic co-gravitation of quanta
      4. 7.4 Temporally transient black objects
    4. 8 Cosmology
      1. 8.1 A synopsis of Big Bang cosmology
      2. 8.2 Dynamic de Sitter cosmology
      3. 8.3 Co-gravitating quanta on dynamic cosmology
      4. 8.4 Cosmological fluctuations
      5. 8.5 Time in cosmology
    5. 9 Gravitation of interacting systems
      1. 9.1 A charged geometry
      2. 9.2 Self-gravitating charged canonical proper-time systems
      3. 9.3 Gravitation of interacting spinors
  11. Appendix A: Addendum for Chapter 1
  12. Appendix B: Addendum for Chapter 2
  13. Appendix C: Addendum for Chapter 3
  14. Appendix D: Addendum for Chapter 4
  15. Appendix E: Addendum for Chapter 5
  16. Appendix F: Addendum for Chapter 7
  17. Appendix G: Addendum for Chapter 8
  18. References
  19. Index