Kiefer C. Quantum gravity

x
CONTENTS
4.2.2 Hamiltonian form of the Einstein–Hilbert action 109
4.2.3 Discussion of the constraints 114
4.2.4 The case of open spaces 118
4.2.5 Structure of configuration space 120
4.3 Canonical gravity with connections and loops 124
4.3.1 The canonical variables 124
4.3.2 Discussion of the constraints 127
4.3.3 Loop variables 130
5 Quantum geometrodynamics 133
5.1 The programme of canonical quantization 133
5.2 The problem of time 136
5.2.1 Time before quantization 138
5.2.2 Time after quantization 141
5.3 The geometrodynamical wave function 144
5.3.1 The diffeomorphism constraints 144
5.3.2 WKB approximation 147
5.3.3 Remarks on the functional Schrödinger picture 148
5.3.4 Connection with path integrals 151
5.3.5 Anomalies and factor ordering 153
5.3.6 Canonical quantum supergravity 158
5.4 The semiclassical approximation 164
5.4.1 Analogies from quantum mechanics 164
5.4.2 Derivation of the Schrödinger equation 170
5.4.3 Quantum-gravitational correction terms 175
6 Quantum gravity with connections and loops 181
6.1 Connection and loop variables 181
6.1.1 Connection representation 181
6.1.2 Loop representation 184
6.2 Quantization of area 189
6.3 Quantum Hamiltonian constraint 194
7 Quantization of black holes 199
7.1 Black-hole thermodynamics and Hawking radiation 199
7.1.1 The laws of black-hole mechanics 199
7.1.2 Hawking and Unruh radiation 201
7.1.3 Bekenstein–Hawking entropy 208
7.2 Canonical quantization of the Schwarzschild black hole 209
7.2.1 Classical formalism 210
7.2.2 Quantization 213
7.3 Black-hole spectroscopy and entropy 217
7.4 Quantum theory of collapsing dust shells 221
7.4.1 Covariant gauge fixing 222
7.4.2 Embedding variables for the classical theory 223