Quantum gravity / Claus Kiefer.

Format:

Book

Author/Creator:

Kiefer, Claus, 1958-

Contributor:

Craig M. Merrihue Memorial Fund.

Series:

International series of monographs on physics (Oxford, England) ; 124.

Oxford science publications

International series of monographs on physics ; 124

Language:

English

Subjects (All):

Quantum gravity.

Physical Description:

ix, 308 pages : illustrations ; 24 cm.

Place of Publication:

Oxford : Clarendon Press ; New York : Oxford University Press, 2004.

Contents:

1 Why quantum gravity? 1

1.1 Quantum theory and the gravitational field 1

1.1.2 Main motivations for quantizing gravity 2

1.1.3 Relevant scales 4

1.1.4 Quantum mechanics and Newtonian gravity 7

1.1.5 Quantum field theory in curved space-time 12

1.2 Problems of a fundamental semiclassical theory 14

1.3 Approaches to quantum gravity 20

2 Covariant approaches to quantum gravity 23

2.1 The concept of a graviton 23

2.1.1 Weak gravitational waves 23

2.1.2 Gravitons from representations of the Poincare group 28

2.1.3 Quantization of the linear field theory 31

2.2 Path integrals and the background-field method 36

2.2.1 General properties of path integrals 36

2.2.2 Background-field method 40

2.2.3 Effective action and Feynman rules 44

2.2.4 Some general remarks on path integrals in perturbation theory 52

2.3 Quantum supergravity 57

3 Parametrized and relational systems 61

3.1 Particle systems 61

3.1.1 Parametrized non-relativistic particle 61

3.1.2 Some remarks on constrained systems 64

3.1.3 The relativistic particle 66

3.2 The free bosonic string 69

3.3 Parametrized field theories 74

3.4 Relational dynamical systems 80

4 Hamiltonian formulation of general relativity 85

4.1 The seventh route to geometrodynamics 85

4.1.1 Principle of path independence 85

4.1.2 Explicit form of generators 87

4.1.3 Geometrodynamics and gauge theories 90

4.2 The 3+1 decomposition of general relativity 92

4.2.1 The canonical variables 93

4.2.2 Hamiltonian form of the Einstein-Hilbert action 95

4.2.3 Discussion of the constraints 101

4.2.4 The case of open spaces 105

4.2.5 Structure of configuration space 106

4.3 Canonical gravity with connections and loops 110

4.3.1 The canonical variables 110

4.3.2 Discussion of the constraints 113

4.3.3 Loop variables 116

5 Quantum geometrodynamics 118

5.1 The programme of canonical quantization 118

5.2 The problem of time 121

5.2.1 Time before quantization 122

5.2.2 Time after quantization 125

5.3 The geometrodynamical wave function 128

5.3.1 The diffeomorphism constraints 128

5.3.2 WKB approximation 131

5.3.3 Remarks on the functional Schrodinger picture 132

5.3.4 Connection with path integrals 135

5.3.5 Anomalies and factor ordering 137

5.3.6 Canonical quantum supergravity 142

5.4 The semiclassical approximation 149

5.4.1 Analogies from quantum mechanics 149

5.4.2 Derivation of the Schrodinger equation 154

5.4.3 Quantum-gravitational correction terms 159

6 Quantum gravity with connections and loops 165

6.1 The Gauss and diffeomorphism constraints 165

6.1.1 Connection representation 165

6.1.2 Loop representation 167

6.2 Quantization of area 171

6.3 Quantum Hamiltonian constraint 176

7 Quantization of black holes 179

7.1 Black-hole thermodynamics and Hawking radiation 179

7.1.1 The laws of black-hole mechanics 179

7.1.2 Hawking and Unruh radiation 181

7.1.3 Bekenstein-Hawking entropy 187

7.2 Canonical quantization of the Schwarzschild black hole 188

7.2.1 Classical formalism 189

7.2.2 Quantization 191

7.3 Black-hole spectroscopy and entropy 196

7.4 Quantum theory of collapsing dust shells 199

7.4.1 Covariant gauge fixing 199

7.4.2 Embedding variables for the classical theory 200

7.4.3 Quantization 204

8 Quantum cosmology 208

8.1 Minisuperspace models 208

8.1.2 Quantization of a Friedmann universe 210

8.1.3 (2+1)-dimensional quantum gravity 220

8.2 Introduction of inhomogeneities 222

8.3 Boundary conditions 226

8.3.1 DeWitt's boundary condition 226

8.3.2 No-boundary condition 227

8.3.3 Tunnelling condition 230

8.3.4 Comparison of no-boundary and tunnelling wave function 232

8.3.5 Symmetric initial condition 234

9 String theory 235

9.2 Quantum gravitational aspects 240

9.2.1 The Polyakov path integral 240

9.2.2 Effective actions 244

9.2.3 T-duality and branes 247

9.2.4 Superstrings 251

9.2.5 Black-hole entropy 254

9.2.6 Brane worlds 257

10 Quantum gravity and the interpretation of quantum theory 262

10.1 Decoherence and the quantum universe 262

10.1.1 Decoherence in quantum mechanics 263

10.1.2 Decoherence in quantum cosmology 265

10.1.3 Decoherence of primordial fluctuations 273

10.2 Arrow of time 274

10.3 Outlook 278.

Notes:

Includes bibliographical references (pages 282-304) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

0198506872

OCLC:

56334605