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Wald R.M. — Quantum field theory in curved spacetime and black hole thermodynamics
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: en

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
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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
$a, a^{\dagger}$ annihilation and creation operators      22 194
$D(\Sigma)$ domain of dependence of $\Sigma$      55
$g_{ab}$ spacetime metric      1
$h^{+}$ future horizon      134
$T_{ab}$ stress-energy tensor of $\phi$      85
$\hat{\phi}(f)$ Klein — Gordon (smeared) field operator      45 59
$\jmath^{+}$, $\jmath^{-}$ null infinity      133
$\kappa$ surface gravity      121
$\mathbf{h}_{A}, \mathbf{h}_{B}$ portions of a bifurcate Killing horizon      120
$\mathcal{A}$ Weyl algebra      74
$\mathcal{A}_{\mathcal{O}}$ subalgebra of $\mathcal{A}$ associated with spacetime region $\mathcal{O}$      84
$\mathcal{D}(\mathcal{O})$ domain of determinacy of $\mathcal{O}$      84
$\mathcal{F}_{s}(\mathcal{H})$ symmetric Fock space      192
$\mathcal{H}$ one-particle Hilbert space      25 27 33 38 40—42 58 63
$\mathcal{H}_{in}$ "in" one-particle Hilbert space      64
$\mathcal{H}_{out}$ "out" one-particle Hilbert space      64
$\mathcal{S}$ vector space of (real) classical solutions      13 36—37 57—58
$\mathcal{S}^{\mathds{C}}$ complexification of $\mathcal{S}$      24
$\mathcal{S}_{\mathcal{O}}$ subspace of classical solutions associated with spacetime region $\mathcal{O}$      84
$\mathcal{S}_{\mu}$ Cauchy completion of $\mathcal{S}$ in the inner product $\mu$      41
$\mathcal{T}$ space of "test functions"      43 58
$\mathfrak{M}$ phase space      11 36 57
$\mu$ inner product on $\mathcal{S}$ used for the construction of $\mathcal{H}$      29 41 58
$\Omega$ symplectic structure on $\mathfrak{M}$ or $\mathcal{S}$      14—15 37 58 140 also
$\Omega(y,\cdot)$ function (or corresponding quantum observable) on $\mathfrak{M}$ or $\mathcal{S}$ obtained from $\Omega$      15
$\overline{\mathcal{H}}$ complex conjugate space to $\mathcal{H}$      190—191
$\phi$ Klein — Gordon scalar field      32 54
$\pi$ momentum density      36 57
$\widehat{\Omega}(\psi,\cdot)$ quantum observable corresponding to $\Omega(\psi,\cdot)$      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 $\mathcal{S}$ to $\mathcal{H}$      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 $h_{a}$      109 122—123
v Killing parameter on $h_{a}$      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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