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Fulling S. Aspects of Quantum Field Theory in Curved Spacetime
Fulling S.  Aspects of Quantum Field Theory in Curved Spacetime









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: Aspects of Quantum Field Theory in Curved Spacetime

: Fulling S.

:

Designed for self-study or advanced courses in relativity and quantum field theory, this introduction arose from a graduate level course and assumes some knowledge of general relativity and differential geometry.


: en

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: 1989

: 320

: 02.09.2005

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$C^{\propto}$, $C_{0}^{\propto}$      2123
$\mathcal{I}$      see null infinity
Abel summation      110
Abramowitz & Stegun (1968)      16
Absolute derivative      173175 179 196
action      1 68 116120 126
Acyclic graph      183
Adiabatic construction of states      153158 208
Adler & Lieberman (1978)      204
Adler et al. (1977)      204
Aharonov Bohm effect      159
Airy function      42
Allen et al. (1988)      185
Allendoerfer (1940)      214
Ambjorn & Wolfram (1983)      221
Anderson & Parker (1987)      213
angular momentum      52 54 224 242 258263 266 268269 279280
Angular velocity      269
Anisotropic expansion      see Bianchi Type I space-time
Annihilation operator      see Creation/annihilation operators
Anti-de Sitter space      122123 176
Anticommutator      80 125126 148149 279
Antiparticle(s)      230 235238 247248 256 267268 274
Approximate eigenvalue      28
Arbuzov & Rochev (1972)      252
Arc length      175183 201 208
Ashtekar & Magnon (1975a)      128 226
Ashtekar & Magnon (1975b)      128
Asymptotics for ODEs      140 151156
Asymptotics for PDEs      158
Asymptotics of heat kernel      193202
Asymptotics of quantum gravity      218
Asymptotics, spectral      106 108 113
Atiyah, M.      202
Atiyah, M. et al. (1973)      108
Atom(s)      28 109 258
Avis et al. (1978)      122
Axioms      53 126
Axioms, Wald      185188 213
Axioms, Wightman      91 127
Bag model      114
Balian & Bloch (1970, 1972, 1974)      108
Banks (1985)      218
Barth & Christensen (1983)      195
Beals (1967)      32
Bekenstein (1973)      258
Bekenstein (1973) & Meisels (1977)      148
Bell & Leinass (1983)      131
Bender & Hays (1976)      114
Berezansky (1968)      32
Bergmann, P.      126
Bernoulli numbers      100
Bessel function      55 85 90 98 208
Bianchi identity      171
Bianchi Type I space-time      135 137 150151
Bilodeau (1977)      221
Birrell (1978)      153
Birrell (1978) & Davies (1982)      128 185 212 214
Bisognano & Wichmann (1975)      131
Bjorken & Drell (1964)      223
Bjorken & Drell (1965)      85 149 223
Black hole      36 123 131 148 219 248 258285
Bloch (coauthor)      287 288
Blum (1973)      226
Bogndr (1974)      229
Bogolubov & Shirkov (1959)      85 149
Bogolubov et al. (1975)      82 87 90 91 148
Bogolubov transformation      139153 157 256 263 276279
Bokobza-Haggiag (1969)      195
Bonazzola & Pacini (1966)      226
Bonic (1969)      200
Borel construction      205
Bosons      see Statistics
Bott (coauthor)      287
Boulware (1975a)      131 285
Boulware (1975b)      131
Boulware (1979)      194
Bound state(s)      28 35 237239 273
Boundary condition(s)      2327 3133 40 4951 103 108 111114 122 124 200203 205 228 232 260
Boundary condition(s), regular      32 34 39 46
Boyer, R. & Lindquist (1967)      259
Boyer, T. (1970)      109 111
Brill et al. (1972)      259
Brown & Ottewill (1986)      185 205 212
Brown (1978)      216
Brown (1984)      185 205 213
Brownell (1955)      113
Bunch & Davies (1978)      212
Bunch (coauthor)      290
Bunch et al. (1978)      153 156 208 212 213
Bunch et al. (1980)      118
c-number      81
Callan et al. (1970)      94
Campbell (1972)      155
Candelas & Deutsch (1977, 1978)      131
Candelas & Howard (1984)      218
Candelas & Raine (1976)      285
Candelas (1980)      218
Candelas (1982)      111 200
Candelas (coauthor)      291 295
Canonical formalism      116120 125128 229 242 245 Momentum canonical)
Canonical formalism, not for fermions      148
Carter (1968)      259
Casimir (1948)      109
Casimir effect      96115 122 184185 199 208
Casimir effect in sphere      111114
Casimir effect, two-dimensional      107
Castagnino & Harari (1984)      185 205 213
Cauchy problem      24 69 7879 120125 190191 210 228 263
Cauchy surface      121124 127131 144 150 211
Causal curve      121
Causal domain      98
Causal propagator      76 7879 81 147 204 206207
Causality      186
Chain rule      89
Chakraborty (1973)      155
Charge      93 109110 228 230231 238239 241243 245247 250 256257 260 268 279 281283
Charge conjugation      232 251 267
Charge, unit      162
Charge-current density      93 157 186 218 224 239 279 281282
Charged field      228 267
Charged field as section      167
Chern (1944, 1945, 1962)      214
Chernoff (1973)      132 226
Choquet Bruhat (1968)      50 98 121 124
Choquet Bruhat (1968) et al. (1977)      130
Christensen & Fulling (1977)      131
Christensen & Parker (1989)      180
Christensen (1976)      174 194 207 208
Christensen (1978)      194 207
Christensen (coauthor)      288 289 290
Christensen series      207208 211212 215
Christoffel symbols      117 162 165166 168 188 Covariant
Chrzanowski & Misner (1974)      274
Chrzanowski (coauthor)      259
Clark (1967)      108
Classical mechanics      1 3 9 1718 33
Classical solutions as eigenfunctions      30
Closed causal curve      122
Closed classical paths      108
Coincidence limit      178 180
Coleman & Weinberg (1973)      215
Coleman (coauthor)      289
Commutation relations      6 10 15 6768 119120 122127 137 145 148 242 245
Commutation relations of Newton Wigner field      7273
Commutation relations, covariant      125
Commutator      4 60 7780 85 91 102 124125 149 170171 186
Compact manifold      131 147
Completeness, geodesic      122 130131
Completeness, geodesic, in vector space      30 32 35 56 228229 231 273
Complex conjugate      3 65
Complex frequency      226 228 231 233 235236 239243 246247 250255 273
Complex structures      128 192
Computers      180 182
Condensed-matter physics      218
Conductors      see Casimir effect
Configuration space      1
Conformal coupling      118 133 137 198 266
Conformal invariance      118 133 135 137 198 213
Conformally flat space      134 216
Conformally related metrics      122123 130 133
Conjugate momentum      see Momentum canonical
Connected graph      183
Connection (form)      23 27 47 161 165 174 191192
Connection (form) on dual space      166167
Connection (form) on tensors      see Tensors differentiation
Connection (form), Levi-Civita      see Christoffel symbols
Connection (form), metric-compatible      172173
Conservation law      9394 185188 212213 216 228 230 238 246 259 268
Consistency axiom      187
Constraints      126
Constructive field theory      219
Continuous spectrum      56 11 2733 41 46 52 62 98 228 230231 243 245 247 255256
Continuous spectrum, absolutely      32
Contractions      183
Coordinate basis      163 170
Corns (coauthor)      297
Cosmological constant      214215
Coulomb potential      189
Counterterms      118119
Coupling constant      118 185 188 214215 243
Covariance      161 166 215
Covariant derivative      117 159167 173 188 194195 Connection Gauge Synge Taylors covariant)
Covariant derivative and parallel transport      174175
Creation/annihilation operators      89 1314 5961 6466 7071 82 128 136137 140 186187 229231 247 261 267 278 280 283
Critchley (coauthor)      295
Current      see Charge-current density Flux
Curvature      117 166173 193195
Curvature, constant      135136
Curvature, principal      112
Curvature, scalar      117 132133 198 266
Cyclic identity      171
d$\Gamma$      6364
Davies, B. (1972)      111
Davies, P. (1974)      282
Davies, P. (1974) (coauthor)      285 288 289
Davies, P. (1974) et al. (1977)      208 212
Davies, P. (1974), (1975)      285
Davies, P. (1974), (1977)      185
De Sitter space      131
De Witt-Morette (coauthor)      290
Dean & Fulling (1982)      47
Delta function      2829 40 4546 62 8788 90 99 120 125 190 206 230 272 275
Density on hypersurface      120 (see also Charge-current density Energy Measure)
Destruction of particles      148
Detector, model      92 283
Determinant of fundamental form      113
Determinant of fundamental form, Van Vleck-Morette      199200
Detweiler & Ipser (1973)      259 269
Deutsch & Candelas (1979)      111 200
Deutsch & Najmi (1983)      128 138
Deutsch (coauthor)      289
DeWitt, B.      147
DeWitt, B. & Brehme (1960)      199 204
DeWitt, B. (1965)      125 173 174 176 180 188 194 207
DeWitt, B. (1975)      36 104 128 207 214 224 258
DeWitt, B. (1984)      125
Diagonal set or value      104 178 210 211
Dieloctrirs      110
Dilations      243
Dillard-Bleick (coauthor)      290
DIMENSION      197198 205
Dimensional analysis      155 193 232233
Dimensional transmutation      215
Dimensionless parameters      18
Dimock, J.      219
Dimock, J. & Kay (1986, 1987)      131
Dimock, J. (1979)      146
Dimock, J. (1980)      50 79 91 124 127 138 139 219
Dimock, J. (1982)      127 219
Dirac distribution      see Delta function
Dirac equation      48 149 161 223
Dirac field      221 237
Dirac notation      34
Direct integral      29
Direct sum      5758 127
Directional derivative      170
Dirichlet condition      25 32 97 103 106107 109 201 232
DiSessa (1974)      285
Disjoint union      5758
Distributions      31 50 5657 62 6467 74 82 8590 9596 99100 144 146147 185
Distributions, integration of      8384
Divergence of vector field      47 94
Domain      23 60
Dowker (1978)      131
Dowker (1978) (coauthor)      295
Drager (1978)      180 195
Drell (coauthor)      223 288
Dual space, connection on      166167 169
Duff, M.      218
Duff, M. (1981)      214 219
Duistermaat & Guillemin (1975)      108 202
Dunford & Schwartz (1963)      38
dAlembertian      117
Eguchi et al. (1980)      200
Eidelman (1969)      188 191
Eigenfunctions      1113 16 20 2223 3047 51 70 136 211 213 225
Eigenvector(s)      11 22 25 28 31 34. 228
Einstein equation      118 166 185 214 218
Einstein tensor      214
Einstein, A.      148
Electromagnetism      48 9293 106 109114 159162 166 169 174 186 189 219 221 223257 260261 265268
Electron      111 148 186
Elliptic equation or operator      10 2047 49 132133 188189 200206
Elliptic regularity      22 31 206
Ellis (coauthor)      259 294
Energy      2 12 15 28 48 54 9396 108109 114 187 228 230231 241242 245247 255259 268 279283
Energy density      39 104108 141 152 156157 209 279284
Energy space      62
Energy, negative      16 48 224 231 238239 241 247 250 252 256 258 284
Energy-momentum tensor      see Stress tensor
Epstein (1975)      216
Equation of motion      12 6 93
Ergosphere      258262
Euler Lagrange equation      1 68 117118
Exclusion principle      148
exercises      19 23 26 40 42 55 57 60 68 84 87 91 98 107 117 119 120 125 132 133 138 139 141 146 155 165 167 169 172 175 181 183 187 191
Exercises, solution      47
Expanding Universe      134 148
expectation value      3 7 92 96 103 127 149 185188 207208 211212 241 280282
Extensions of operator      2427
External field or potential      21 188 191 197 210211 284
Fackerell (coauthor)      259
Fedoriuk (coauthor)      296
Fermi coordinates      285
fermions      221 (see also Statistics)
Feshbach & Villars (1958)      226
Feynman diagrams      81
Feynman function      see Causal propagator
Fiber      161 163 182 191193 197 199
Field      9 15 1920 4849 55 73 92 158 163164 217219 224 283
Field algebra      6 19 6970 91 124127 150 219 241 247
Field operator      6470 80 127 136 144 246 267 280
Fierz (1960)      107
Figari et al. (1975)      131
figures      14 16 17 36 37 38 44 75 76 77 79 89 97 102 108 109 112 121 122 123 124 131 138 163 177 186 201 204 209
Figures, appendix      232 237 249 251 254 262 264
Finite propagation speed      79 206
Finite-size effect      103104 106108
First-order formalism      226 (see also Stationary space-time)
1 2 3 4
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