Cambridge University Press 978-1-107-00840-3 - Foundations of Quantum Gravity James Lindesay Index More information Index abelian, 374 basis vectors, 48, 207 abelian group, 357 beginning of time, 313 abelian subgroup, 353 Belinfante tensor, 131, 256 absolute motion, 222 Bell’s inequality, 67 absolute space, 222 Bianchi identities, 218 accelerating observer, 229 Big Bang cosmology, 309 accelerating oscillator, 40 Birkhoff’s theorem, 89, 270 quantum, 365 black body, 310, 320 acceleration, 24, 205 black body radiation, 126 thermal properties, 96 black hole, 261, 267, 295 acoustic wave, 310 charged, 349 primordial, 332 dynamic, 281 action, 128 extremal, 350 Euclidean, 387 non-singular, 271 gravitational, 225 Schwarzschild, 270, 274 action principle, 210, 223 spatially coherent, 282 active transformations, 14 temporally transient, 294 adiabatic expansion, 320 threshold mass, 261 adjoint representation, 158, 359 black object, 268, 295 affine connections, see connections,36 temporally transient, 294 affine mass, see transverse mass, 172 blue shift, 209 affine parameter, 215 Bohr gravitating system, 90 affine space, 207 Boltzmann’s entropy, 77 affine translations, 176 Bose–Einstein condensate, 145 algebra, 133 bosons, 69 analyticity, 28 bound state wavefunction, 106 anelastic scattering, 120 bound states, 104, 108 angular momentum, 130, 132 boundary conditions, 223 canonical, 132 boundary states, 104 Kerr geometry, 241 bra, 48 angular momentum conservation, 132 breakup, 116 annihilation operator, 59 anti-commutator, 51, 55 calculating curvature, 384 arbitrariness of coordinate systems, calculus of variations, 128 206 canonical ensemble, 78, 276 area theorem canonical momentum, 41 violation, 248 canonical proper-energy, 37 artificial gravity, 34 canonical proper-time, 36 associativity, 51, 357 Casimir effect, 60 Asymptopia, 240 Casimir operator, 360 average, 54 Cauchy principal value, 115 397 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-00840-3 - Foundations of Quantum Gravity James Lindesay Index More information 398 Index causal horizon, 31 complementary set, 159 causal patch, 26 completeness, 48 causal propagator, 113 Compton scattering, 120 causal resolvant, 123 cosmological, 332 causal spinor field, 185, 198 condensed-matter fields, 72 causality, 43, 184, 226, 278 confinement, 104, 117 centrifugal barrier, 251 conformal coordinates, 28, 42 chain rule, 206, 207, 209, 383 de Sitter space, 315 Chandrasekhar limit, 310 spatially coherent black hole, 282 channel decomposition, 106 conformal diagrams, 42 charge, 18 dynamic de Sitter, 327 conservation, 346 stellar, 233 generalized, 134 conformal mass, see transverse mass, 379 charge conjugation, 178, 195 conformal time, 332 spinor fields, 197, 200 conical angle, 277 charge conservation, 130 conical excess, 387 charge current density connections, 36, 209, 211, 212, 257, 383 with gravity, 347 trace, 213 charge quantization, 22 conservation equations, 129 charged geometry, 345 of angular momentum, 220 chiral projections, 380 of charge, 18 chirality, 171 with gravity, 346 Christoffel symbols, 36 of energy, 220 classical correspondence, 56, 101, 119 of energy-momentum, 129 classical disentanglement, 122 of probability, 101 classical gravitation, 40 of velocity, 110 classical-quantum correspondence, 56 properties, 101 cloning, 83 conservative forces, 218 closed forms, 383 contact form of relativistic dynamics, 111 closed universe, 311 continuity equation, 18, 129 closure, 51, 133, 357 current density, 130 cluster decomposability, 101, 110, 111, 252, 287 fluid, 232 cluster decomposition, 65, 120 photons, 332 clusters, 104 continuum states, 105 CMB radiation (cosmic microwave background contravariant vector, 13, 207 radiation), 267, 310 convergence of QED, 103 fluctuations, 332 Cooper pair, 102 co-gravitating masses, 263 coordinate basis, 207 co-gravitating quanta, 288 coordinate geometry, 216 co-gravitation, 88, 92, 246, 287, 332 coordinate singularity, 237 Klein–Gordon fields, 287 coordinates not vectors, 210 co-moving, 230 core gravitating field, 291 co-moving observers, 312, 318, 329 correlation functions, 73 coalescence, 116 photons, 127 coarse-grained measurements, 79 correlations, 60, 72, 73 coherence, 54, 81, 245 correspondence, 38, 110, 112, 117, 182, 213, 220, coherence functions 228, 241, 339 photon, 127 correspondence problem, 104 coherence rule, 246 cosmic microwave background radiation, see CMB collapse radiation pressureless, 296 cosmological collapse of the wave function, 54 constant, 221, 311, 313 color, 135 densities, 311 commutator, 51, 55 features, 311 commuting operators, 51 parameters, 337 compact, 361 principle, 309, 317 compact coordinates, 44 cosmology, 309 complementarity, 269, 278, 307 counting of bound states, 369 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-00840-3 - Foundations of Quantum Gravity James Lindesay Index More information Index 399 covariance, 246, 267 Einstein summation convention, 12 covariant derivative, 212 Einstein tensor covariant divergence, 213 spatially coherent black hole, 282 covariant vectors, 207 Einstein’s equations, 220 covering group, 357, 362, 363 quantum, 246 CP transformation, 200 self-generating mass, 261 Cramer’s rule, 255 Einstein’s relation, 326 creation operator, 59 elastic scattering, 117 cross section, 115 electrodynamics, 18 crossing, 124 electromagnetic CTP theorem, 201 energy density, 21 CTP transformation, 200, 201 energy-momentum, 21 current density, 21, 130 field tensor, 20 curvature, 216 momentum density, 22 calculation, 384 radiation field, 70 curvature two-forms, 384 electromagnetism, 137 curved space-time backgrounds, 245 on curved space-times, 346 curvilinear coordinates, 206, 211 emergence of space-time, 246 empty space, 220 dark energy, 309, 311, 340 energy, 15 dark energy domination, 328 energy conditions, 95, 226, 248 dark energy partitions, 335 fluids, 236 dark matter, 310 self-gravitating masses, 263 de Sitter space, 314 energy conservation, 220 decoupling, 323 energy density, 220 degree of mapping, 145, 148 energy flux, 220 density matrix, 74, 278, 289, 339 energy-momentum conservation, 221, 231 Rindler, 279 energy-momentum tensor, 132, 136, 221 Schwarzschild, 280 core gravitating field, 292 density of states, 61, 276, 337 electromagnetic, 345 density perturbations fluid, 231 primordial, 333 gauge fields, 136 determinant and trace, 213 gravitation, 225 diagonal coordinates, 230 gravitational, 255 diffusion constant, 325 linear spinor fields, 255 dimensional analysis, 290, 293 symmetric, 131 dimensions, units, 206 entanglement, 65, 74, 80, 82, 110 Dirac sea, 168, 189 black object geometry, 306 disconnected diagrams, 106 entanglement entropy, 81 discrete symmetries, 173 entropy, 275 disentangled states, 120 black holes, 277, 387 disentanglement, 252, 287 cosmological, 340, 341 disorder, 79 horizon, 340 dispersion relation, 189 statistical, 78 dissipation, 389 thermal, 77 distant correlations, 67 von Neumann, 77 divergences, 247 entropy bounds, 280 dominant energy condition, 226 entropy per baryon, 312 dual of a spinor, 151 Eotvos experiment, 205 dust equation of state, 320 equatorial motions, Kerr geometry, 242 dynamic de Sitter cosmology, 316, 317 equivalence principle, 199, 205, 209, 214, 225, 246 dynamic geometries, 345 equivalent vector representation, 373 eternal triangle, 108 effective range, 108 Euclidean metric, 276 Efimov effect, 102, 108, 371 Euler equation, 332 eigenstate, 50, 53 Euler–Lagrange equations, 129 eigenvalue, 50 gauge fields, 136 Einstein field equations, 221, 339, 340 local, 136 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-00840-3 - Foundations of Quantum Gravity James Lindesay Index More information 400 Index evaporation, 274 future light cone, 43 black object, 297, 307 future light-like infinity, 45 event horizon, see horizon, 270 exact forms, 383 Galilean group, 139, 140 exotic motions, 239 Galilean pre-symmetry, 142 expansion rate Gamma boosts, 379 initial, 335 gauge covariant derivative, 134, 144 expectation value, 50, 55, 74 gauge current non-conservation, 136 extended Poincare´ group, 254 gauge currents, 136, 138 exterior derivative, 383 gauge invariance, 135 extracting poles, 106 gauge potentials, 134 extremal black hole, 350 transformation, 134 gauge transformations, 133, 142 Faddeev channels, 111 general relativity, 205 Faddeev formulation of scattering theory, 106 general relativity as a local theory, 330 Fermi degeneracy pressure, 310 generators, 51, 129, 133, 207, 218 fermions, 69 generators for infinitesimal transformations, 51, 358, few particle scattering theory, 110 360 fiducial observers, 38, 209, 229, 271 geodesic equation, 36, 209, 214, 257 charged geometry, 350 geodesic motion field strengths, 134 cosmological, 324 fine-grained measurements, 79 spatially coherent black hole, 284 first law of thermodynamics, 77, 275, 341 geodesics, 205, 208, 210, 257 Big Bang, 320 geometric conservation, 221 black holes, 277 geometric consistency, 300 dynamic de Sitter, 321 cosmology, 334 fluctuations, 332, 389 geometric kinematic invariants, 218 CMB, 310 geometric time, 339 zero-point, 336 geometrically stationary observers, 230, 259, 313 fluid cosmology, 316 dynamic de Sitter, 317, 329 fluid densities, 231 Robertson–Walker, 318 fluid dynamics spatially coherent black hole, 285 cosmology, 318 transient black object, 304 fluid, ideal, 231 geometrodynamics, 220 force density, 137 global positioning satellites, 227 four-current density, 21 global