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Wald R.M. Ч Quantum field theory in curved spacetime and black hole thermodynamics
Wald R.M. Ч Quantum field theory in curved spacetime and black hole thermodynamics

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Ќазвание: Quantum field theory in curved spacetime and black hole thermodynamics

јвтор: Wald R.M.

јннотаци€:

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.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1994

 оличество страниц: 220

ƒобавлена в каталог: 02.11.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"In" representation      64
"In" representation for black hole      153
"Out" representation      64
"Out" representation for black hole      153Ч154 157 179Ч180
"Point-splitting" regularization      87Ч88 91Ч94 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 Ч 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 40Ч42 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 36Ч37 57Ч58
$\mathcal{S}^{\mathds{C}}$ 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 $\mathcal{S}$      14Ч15 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 $\mathcal{H}$      190Ч191
$\phi$ Klein Ч 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      73Ч85
Algebraic formulation for fermion fields      104
Angular velocity of horizon      140
Annihilation operator      22 194
Antilinear map      188
Area theorem      137Ч139
Asymptotic completeness      153 154Ч155
Back-reaction      86 98Ч100
Back-reaction for black holes      175Ч177 186Ч187
Baryon nonconservation      177Ч178
Bifurcate Killing horizon      120 120Ч123 140Ч141
Black holes      6Ч8 133Ч134
Black holes area theorem      137Ч139
Black holes, classical properties of      133Ч150
Black holes, evaporation of      175Ч187
Black holes, particle creation by      152Ч163
Black holes, predictable      137
Black holes, thermodynamic laws of      7Ч8 139Ч150 163Ч175
Bogoliubov transformation      69
Boulware vacuum      126 128 160Ч161
Buoyancy force      168Ч171
C*-algebra      190
C*-algebra, net of      84
C,D operators arising in solving for the S-matrix      68
Cauchy surface      55Ч56
Charged scalar field      101Ч103
Coherence, quantum, loss of      178Ч185 187
Commutation relations of annihilation and creation operators      22 194
Commutation relations of fundamental quantum observables      18 37 45Ч46
Complex conjugate space      190
Complex structure      41
Cosmic censorship      135Ч137
Creation operator      194
Cyclic vector      76
Density matrix in Hawking effect      179Ч180
Density matrix in Unruh effect      115
DeSitter spacetime      127Ч128
DeWitt-Schwinger expansion      93
Dilaton gravity      185Ч187
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      145Ч147
Entropy of black hole      163Ч164
Entropy, generalized      166
Euclidean methods      129Ч132 164Ч166
Event horizon      134 137Ч139 140Ч141
Fell's theorem      81
Fermion fields      103Ч104
Feynmann propagator      130 130Ч132
Field operator      45 59
First law      141Ч147
Fock space      192
Folium      76
Fundamental observables      74
Generalized second law      166 166Ч175
Global hyperbolicity      56
GNS construction      76
Green's functions      43Ч46 56 58 93 130Ч132
Hadamard bi-distribution      92
Hadamard state      95 95Ч97 125Ч126 161Ч162
Hamiltonian diagonalization      65
Hamiltonian for field-particle detector system      47
Hamiltonian for general relativity      144
Hamiltonian for harmonic oscillator      21Ч22
Hamiltonian in classical mechanics      11Ч13
harmonic oscillator      21Ч30
Hartle Ч Hawking vacuum      128 128Ч129 151 155 161
Hawking effect      8Ч9 151Ч163 157
Hawking temperature      124
Hilbert space      189 see "One-particle ""Out"
Hilbert space for quantum field      33Ч34 38 40Ч43 46 58 102Ч104
Hilbert space in stationary spacetimes      63
Hilbert space, completion      189
Hilbert space, direct sums of      191
Hilbert space, tensor products of      191Ч192
Horizon      134 134Ч135 see "Killing
Index notation      192Ч194
Infra-red divergences      38 61 83 93 97 131
Inner product      189
Inner product, Klein Ч Gordon      38
Interacting fields      see "Nonlinear fields"
Irreducible representation      19 83Ч84
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 120Ч123 140Ч141
Killing horizon, degenerate      141
Killing vector field      118
Klein Ч 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 Ч 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      78Ч81
Mixed state      83 84Ч85
Momentum density      36 57
Noether charge      146
Nonlinear fields      118 132 162Ч163
Norm      188Ч189
Normal ordering      87Ч88
Null energy condition      138
One-particle Hilbert space      25 27Ч30 33Ч34 38 40Ч43 46 51 58 63 103
Particle creation      71
Particle creation by black holes      152Ч163
Particle detector      47Ч51 63 116
Particle, definition of      2Ч4 46Ч52 59Ч60 63Ч64 116 159
Partition function      164
Phase space      11 36 57
Poisson bracket      13Ч14 15 37
Poisson bracket, relationship with commutators      17Ч18 20
Positive frequency      23 25 27 33Ч34 38 40 61 63 71
Positivity condition      74 75
Propagator      see "Feynmann propagator" "Green's "Two-point
Pure state      83 84Ч85
Quasi-free state      77 84
Reeh Ч Schlieder theorem      85
Regularization, of stress-energy tensor      see ""Point-splitting" regularization"
Remnant, of black hole      183Ч184
Riesz lemma      190
Rindler vacuum      107 126
Runaway solution      99Ч100
S-matrix      64 66Ч71 83
S-matrix in Hawking effect      154Ч159
S-matrix in Unruh effect      114
Schwarzschild black hole      128Ч129
Schwarzschild black hole, particle creation by      152Ч163
Second law, area theorem      137Ч139
Second law, generalized      166Ч175
Semiclassical approximation      57 144 see
Shift vector      57 144
Solution space      17 36Ч37 57Ч58 101
Spontaneous emission      51 71
Squeezed vacuum state      29 71
State, algebraic      74
Stationary spacetimes, quantum field theory in      61Ч65
Stimulated emission      51
Stone Ч Von Neumann theorem      20
Stress-energy tensor, quantum      85Ч100 187
Superscattering matrix      180 181
Surface gravity      121 121Ч122 127 128 140 149
Symplectic form      11
Symplectic structure      14Ч15 16Ч17 37 58 101
Temperature, of Schwarzschild black hole      157
Tensor product      191Ч192
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 74Ч75 87Ч88 91Ч94
Two-point function in Hawking effect      159Ч162
Two-point function in Unruh effect      117 130Ч132
U S-matrix      64 66 109 123 also
Unitary equivalence      19 60 66Ч72 73 83 96Ч97
Unitary equivalence in Unruh effect      114
Unruh effect      8 105Ч118 115 123Ч132
Unruh vacuum      158
V affine parameter on $h_{a}$      109 122Ч123
v Killing parameter on $h_{a}$      110 122
Vacuum polarization      88
Vacuum state xii-xiii      50Ч51
Vector space      188
von Neumann algebra      79
Weyl algebra      74
Weyl relations      19 73
Zeroth Law      149
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