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Modern Canonical Quantum General Relativity

$82.99 (C)

Part of Cambridge Monographs on Mathematical Physics

  • Author: Thomas Thiemann, Max-Planck-Institut für Gravitationsphysik, Germany
  • Date Published: December 2008
  • availability: Temporarily unavailable - available from TBC
  • format: Paperback
  • isbn: 9780521741873

$ 82.99 (C)

Temporarily unavailable - available from TBC
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About the Authors
  • Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.

    • Discusses all aspects of theory from the foundations to the frontiers of current research
    • Contains mathematical precision which reaches new levels of rigour
    • Designed to be an absolute reference text on the subject
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    Reviews & endorsements

    "This book is a complete treatise on one approach, loop quantum gravity, to reformulating quantum theory in a background-independent way. It is suitable for graduate students and researchers in theoretical physics with a basic knowledge of quantum field theory and general relativity. Dr. Thiemann brings a deep level of mathematical understanding to the problem and has succeeded in solving some of the most complex problems in the area. The book is a snapshot of the theories in the field that may be leading to a greater understanding of our world.

    "I enjoyed the book very much. The reader who is not mathematically oriented may be worried by some of the parts of the book that are more formal. But Thiemann has a careful writing style in which mathematics is used only as much as needed and always after proper definitions. ... I am convinced the book will immediately become a reference on the subject of loop quantum gravity and its modern developments." - Jorge A. Pullin, Mathematical Reviews

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    Product details

    • Date Published: December 2008
    • format: Paperback
    • isbn: 9780521741873
    • length: 846 pages
    • dimensions: 248 x 174 x 46 mm
    • weight: 1.41kg
    • availability: Temporarily unavailable - available from TBC
  • Table of Contents

    Notation and conventions
    Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme:
    1. Classical Hamiltonian formulation of general relativity
    2. The problem of time, locality and the interpretation of quantum mechanics
    3. The programme of canonical quantisation
    4. The new canonical variables of Ashtekar for general relativity
    Part II. Foundations of Modern Canonical Quantum General Relativity:
    5. Introduction
    6. Step I: the holonomy-flux algebra [P]
    7. Step II: quantum-algebra
    8. Step III: representation theory of [A]
    9. Step IV:
    1. Implementation and solution of the kinematical constraints
    10. Step V:
    2. Implementation and solution of the Hamiltonian constraint
    11. Step VI: semiclassical analysis
    Part III. Physical Applications:
    12. Extension to standard matter
    13. Kinematical geometrical operators
    14. Spin foam models
    15. Quantum black hole physics
    16. Applications to particle physics and quantum cosmology
    17. Loop quantum gravity phenomenology
    Part IV. Mathematical Tools and their Connection to Physics:
    18. Tools from general topology
    19. Differential, Riemannian, symplectic and complex geometry
    20. Semianalytical category
    21. Elements of fibre bundle theory
    22. Holonomies on non-trivial fibre bundles
    23. Geometric quantisation
    24. The Dirac algorithm for field theories with constraints
    25. Tools from measure theory
    26. Elementary introduction to Gel'fand theory for Abelean C* algebras
    27. Bohr compactification of the real line
    28. Operatir -algebras and spectral theorem
    29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID)
    30. Basics of harmonic analysis on compact Lie groups
    31. Spin network functions for SU(2)
    32. + Functional analytical description of classical connection dynamics

  • Author

    Thomas Thiemann, Max-Planck-Institut für Gravitationsphysik, Germany
    Thomas Thiemann is Staff Scientist at the Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Potsdam, Germany. He is also a long-term researcher at the Perimeter Institute for Theoretical Physics and Associate Professor at the University of Waterloo, Canada. Thomas Thiemann obtained his PhD in theoretical physics from the Rheinisch-Westfälisch Technische Hochschule, Aachen, Germany. He held two year postdoctoral positions at The Pennsylvania State University and Harvard University. As of 2005 he holds a guest professor position at Beijing Normal University, China.

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