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Quantum Gravity (Second Edition) by Claus Kiefer



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Quantum Gravity (Second Edition) written by Claus Kiefer , Institute for Theoretical Physics, University of Cologne. The present second edition of this book is an extended and revised version of the first edition. It contains, in particular, new sections on asymptotic safety, dynamical triangulation, primordial black holes, the information-loss problem, loop quantum cosmology, and other topics. The text has been revised throughout.


Quantum Gravity (Second Edition) written by Claus Kiefer cover the following topics.


  • 1 Why quantum gravity?
    1.1 Quantum theory and the gravitational field
    1.1.1 Introduction
    1.1.2 Main motivations for quantizing gravity
    1.1.3 Relevant scales
    1.1.4 Quantum mechanics and Newtonian gravity
    1.1.5 Quantum field theory in curved space–time
    1.2 Problems of a fundamentally semiclassical theory
    1.3 Approaches to quantum gravity

  • 2 Covariant approaches to quantum gravity
    2.1 The concept of a graviton
    2.1.1 Weak gravitational waves
    2.1.2 Gravitons from representations of the Poincar´e group
    2.1.3 Quantization of the linear field theory
    2.2 Path-integral quantization
    2.2.1 General properties of path integrals
    2.2.2 The perturbative non-renormalizability
    2.2.3 Effective action and Feynman rules
    2.2.4 Semiclassical Einstein equations
    2.2.5 Asymptotic safety
    2.2.6 Regge calculus and dynamical triangulation
    2.3 Quantum supergravity

  • 3 Parametrized and relational systems
    3.1 Particle systems
    3.1.1 Parametrized non-relativistic particle
    3.1.3 The relativistic particle
    3.2 The free bosonic string
    3.3 Parametrized field theories
    3.4 Relational dynamical systems

  • 4 Hamiltonian formulation of general relativity
    4.1 The seventh route to geometrodynamics
    4.1.1 Principle of path independence
    4.1.2 Explicit form of generators
    4.1.3 Geometrodynamics and gauge theories
    4.2 The 3+1 decomposition of general relativity
    4.2.1 The canonical variables
    4.2.2 Hamiltonian form of the Einstein–Hilbert action
    4.2.3 Discussion of the constraints
    4.2.4 The case of open spaces
    4.2.5 Structure of configuration space
    4.3 Canonical gravity with connections and loops
    4.3.1 The canonical variables
    4.3.2 Discussion of the constraints
    4.3.3 Loop variables

  • 5 Quantum geometrodynamics
    5.1 The programme of canonical quantization
    5.2 The problem of time
    5.2.1 Time before quantization
    5.2.2 Time after quantization
    5.3 The geometrodynamical wave function
    5.3.1 The diffeomorphism constraints
    5.3.2 WKB approximation
    5.3.3 Remarks on the functional Schr¨odinger picture
    5.3.4 Connection with path integrals
    5.3.5 Anomalies and factor ordering
    5.3.6 Canonical quantum supergravity
    5.4 The semiclassical approximation
    5.4.1 Analogies from quantum mechanics
    5.4.2 Derivation of the Schr¨odinger equation
    5.4.3 Quantum-gravitational correction terms

  • 6 Quantum gravity with connections and loops
    6.1 Connection and loop variables
    6.1.1 Connection representation
    6.1.2 Loop representation
    6.2 Quantization of area
    6.3 Quantum Hamiltonian constraint

  • 7 Quantization of black holes
    7.1 Black-hole thermodynamics and Hawking radiation
    7.1.1 The laws of black-hole mechanics
    7.1.2 Hawking and Unruh radiation
    7.1.3 Bekenstein–Hawking entropy
    7.2 Canonical quantization of the Schwarzschild black hole
    7.2.1 Classical formalism
    7.2.2 Quantization
    7.3 Black-hole spectroscopy and entropy
    7.4 Quantum theory of collapsing dust shells
    7.4.1 Covariant gauge fixing
    7.4.2 Embedding variables for the classical theory
    7.4.3 Quantization
    7.5 The Lemaˆitre–Tolman–Bondi model
    7.5.1 The classical LTB model
    7.5.2 Quantization
    7.6 The information-loss problem
    7.7 Primordial black holes

  • 8 Quantum cosmology
    8.1 Minisuperspace models
    8.1.1 General introduction
    8.1.2 Quantization of a Friedmann universe
    8.1.3 (2+1)-dimensional quantum gravity
    8.2 Introduction of inhomogeneities
    8.3 Boundary conditions
    8.3.1 DeWitt’s boundary condition
    8.3.2 No-boundary condition
    8.3.3 Tunnelling condition
    8.3.4 Comparison of no-boundary and tunnelling wave function
    8.3.5 Symmetric initial condition
    8.4 Loop quantum cosmology
    8.4.1 Classical variables
    8.4.2 Quantization

  • 9 String theory
    9.1 General introduction
    9.2 Quantum-gravitational aspects
    9.2.1 The Polyakov path integral
    9.2.2 Effective actions
    9.2.3 T-duality and branes
    9.2.4 Superstrings
    9.2.5 Black-hole entropy
    9.2.6 Brane worlds

  • 10 Quantum gravity and the interpretation of quantum theory
    10.1 Decoherence and the quantum universe
    10.1.1 Decoherence in quantum mechanics
    10.1.2 Decoherence in quantum cosmology
    10.1.3 Decoherence of primordial fluctuations
    10.2 Arrow of time
    10.3 Outlook
    References
    Index

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