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Wald R.M. — Quantum field theory in curved spacetime and black hole thermodynamics
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Íàçâàíèå: Quantum field theory in curved spacetime and black hole thermodynamics
Àâòîð: Wald R.M.
Àííîòàöèÿ: In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth.
This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum field theory, and will be of interest to scientists in general relativity and related fields.
ßçûê:
Ðóáðèêà: Ôèçèêà /
Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö
ed2k: ed2k stats
Ãîä èçäàíèÿ: 1994
Êîëè÷åñòâî ñòðàíèö: 220
Äîáàâëåíà â êàòàëîã: 02.11.2010
Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
"In" representation 64
"In" representation for black hole 153
"Out" representation 64
"Out" representation for black hole 153—154 157 179—180
"Point-splitting" regularization 87—88 91—94 99
annihilation and creation operators 22 194
domain of dependence of 55
spacetime metric 1
future horizon 134
stress-energy tensor of 85
Klein — Gordon (smeared) field operator 45 59
, null infinity 133
surface gravity 121
portions of a bifurcate Killing horizon 120
Weyl algebra 74
subalgebra of associated with spacetime region 84
domain of determinacy of 84
symmetric Fock space 192
one-particle Hilbert space 25 27 33 38 40—42 58 63
"in" one-particle Hilbert space 64
"out" one-particle Hilbert space 64
vector space of (real) classical solutions 13 36—37 57—58
complexification of 24
subspace of classical solutions associated with spacetime region 84
Cauchy completion of in the inner product 41
space of "test functions" 43 58
phase space 11 36 57
inner product on used for the construction of 29 41 58
symplectic structure on or 14—15 37 58 140 also
function (or corresponding quantum observable) on or obtained from 15
complex conjugate space to 190—191
Klein — Gordon scalar field 32 54
momentum density 36 57
quantum observable corresponding to 26 39 59
Adjoint 191
ADM Hamiltonian 144
Algebra 189
Algebra, C*- 190
Algebra, von Neumann 79
Algebra, Weyl 74
Algebraic formulation 73—85
Algebraic formulation for fermion fields 104
Angular velocity of horizon 140
Annihilation operator 22 194
Antilinear map 188
Area theorem 137—139
Asymptotic completeness 153 154—155
Back-reaction 86 98—100
Back-reaction for black holes 175—177 186—187
Baryon nonconservation 177—178
Bifurcate Killing horizon 120 120—123 140—141
Black holes 6—8 133—134
Black holes area theorem 137—139
Black holes, classical properties of 133—150
Black holes, evaporation of 175—187
Black holes, particle creation by 152—163
Black holes, predictable 137
Black holes, thermodynamic laws of 7—8 139—150 163—175
Bogoliubov transformation 69
Boulware vacuum 126 128 160—161
Buoyancy force 168—171
C*-algebra 190
C*-algebra, net of 84
C,D operators arising in solving for the S-matrix 68
Cauchy surface 55—56
Charged scalar field 101—103
Coherence, quantum, loss of 178—185 187
Commutation relations of annihilation and creation operators 22 194
Commutation relations of fundamental quantum observables 18 37 45—46
Complex conjugate space 190
Complex structure 41
Cosmic censorship 135—137
Creation operator 194
Cyclic vector 76
Density matrix in Hawking effect 179—180
Density matrix in Unruh effect 115
DeSitter spacetime 127—128
DeWitt-Schwinger expansion 93
Dilaton gravity 185—187
Direct sum 191
Domain of dependence 55
Domain of determinacy 84
Dual space 190
E advanced minus retailed Green's function 43
Electromagnetic field, quantum theory of 101
Entropy in general theory of gravity 145—147
Entropy of black hole 163—164
Entropy, generalized 166
Euclidean methods 129—132 164—166
Event horizon 134 137—139 140—141
Fell's theorem 81
Fermion fields 103—104
Feynmann propagator 130 130—132
Field operator 45 59
First law 141—147
Fock space 192
Folium 76
Fundamental observables 74
Generalized second law 166 166—175
Global hyperbolicity 56
GNS construction 76
Green's functions 43—46 56 58 93 130—132
Hadamard bi-distribution 92
Hadamard state 95 95—97 125—126 161—162
Hamiltonian diagonalization 65
Hamiltonian for field-particle detector system 47
Hamiltonian for general relativity 144
Hamiltonian for harmonic oscillator 21—22
Hamiltonian in classical mechanics 11—13
harmonic oscillator 21—30
Hartle — Hawking vacuum 128 128—129 151 155 161
Hawking effect 8—9 151—163 157
Hawking temperature 124
Hilbert space 189 see "One-particle ""Out"
Hilbert space for quantum field 33—34 38 40—43 46 58 102—104
Hilbert space in stationary spacetimes 63
Hilbert space, completion 189
Hilbert space, direct sums of 191
Hilbert space, tensor products of 191—192
Horizon 134 134—135 see "Killing
Index notation 192—194
Infra-red divergences 38 61 83 93 97 131
Inner product 189
Inner product, Klein — Gordon 38
Interacting fields see "Nonlinear fields"
Irreducible representation 19 83—84
Isometry 118
K "projection map" from to 28 38 42
Kerr black hole 127 129 141 149 152
Killing horizon 120 120—123 140—141
Killing horizon, degenerate 141
Killing vector field 118
Klein — Gordon inner product 38
KMS condition 118 126
Lagrangian for dilaton gravity 186
Lagrangian for general theory of gravity 145
Lagrangian for harmonic oscillator 21
Lagrangian for Klein — Gordon field 32 54
Lapse function 57 144
Lifetime, of black hole 177
Linear dynamical system 14
Linear map 188
M spacetime manfold 1
Maxwell field, quantum theory of 101
Measurement theory, in algebraic approach 78—81
Mixed state 83 84—85
Momentum density 36 57
Noether charge 146
Nonlinear fields 118 132 162—163
Norm 188—189
Normal ordering 87—88
Null energy condition 138
One-particle Hilbert space 25 27—30 33—34 38 40—43 46 51 58 63 103
Particle creation 71
Particle creation by black holes 152—163
Particle detector 47—51 63 116
Particle, definition of 2—4 46—52 59—60 63—64 116 159
Partition function 164
Phase space 11 36 57
Poisson bracket 13—14 15 37
Poisson bracket, relationship with commutators 17—18 20
Positive frequency 23 25 27 33—34 38 40 61 63 71
Positivity condition 74 75
Propagator see "Feynmann propagator" "Green's "Two-point
Pure state 83 84—85
Quasi-free state 77 84
Reeh — Schlieder theorem 85
Regularization, of stress-energy tensor see ""Point-splitting" regularization"
Remnant, of black hole 183—184
Riesz lemma 190
Rindler vacuum 107 126
Runaway solution 99—100
S-matrix 64 66—71 83
S-matrix in Hawking effect 154—159
S-matrix in Unruh effect 114
Schwarzschild black hole 128—129
Schwarzschild black hole, particle creation by 152—163
Second law, area theorem 137—139
Second law, generalized 166—175
Semiclassical approximation 57 144 see
Shift vector 57 144
Solution space 17 36—37 57—58 101
Spontaneous emission 51 71
Squeezed vacuum state 29 71
State, algebraic 74
Stationary spacetimes, quantum field theory in 61—65
Stimulated emission 51
Stone — Von Neumann theorem 20
Stress-energy tensor, quantum 85—100 187
Superscattering matrix 180 181
Surface gravity 121 121—122 127 128 140 149
Symplectic form 11
Symplectic structure 14—15 16—17 37 58 101
Temperature, of Schwarzschild black hole 157
Tensor product 191—192
Test functions 43 58 84
Third law 149
Trace anomaly 94
Trapped surface 7 139
Two-dimensional model see "Dilaton gravity"
Two-point Function 46 74—75 87—88 91—94
Two-point function in Hawking effect 159—162
Two-point function in Unruh effect 117 130—132
U S-matrix 64 66 109 123 also
Unitary equivalence 19 60 66—72 73 83 96—97
Unitary equivalence in Unruh effect 114
Unruh effect 8 105—118 115 123—132
Unruh vacuum 158
V affine parameter on 109 122—123
v Killing parameter on 110 122
Vacuum polarization 88
Vacuum state xii-xiii 50—51
Vector space 188
von Neumann algebra 79
Weyl algebra 74
Weyl relations 19 73
Zeroth Law 149
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