Approaches to Quantum Gravity

582 Index
326, 329, 332–336, 373, 379, 395, 396, 403,
430, 431, 436, 437, 443, 444, 509, 511, 513,
514, 517, 528, 537, 549, 555, 558, 559, 561,
562, 566, 567
M-theory, 17, 210, 222, 224
master constraint, 240, 241, 248
matrix models, 157, 177, 178, 232, 310, 319, 417–419
matrix theory, 180, 205, 207, 210, 224
measurement, 46, 47, 50, 52, 53, 254, 511, 514, 515,
517, 518, 525, 530, 543, 576
as a process, 45
continuous, 45
instantaneous, 45
of spacetime geometry, 53, 54, 89, 572
quantum, 91, 151
minimal length, 5, 6, 35, 124, 153, 560
non-commutative field theory, 303–308
non-commutative geometry, 8, 10, 29, 120, 153, 193,
291, 301–303, 306, 321, 429, 431, 432, 436,
437, 443, 444, 466–469, 471, 473, 476, 477,
484–491, 514, 539, 573
observables
Dirac, 241–244, 248, 514
gauge invariant, 179, 187, 190
partial, 7, 512
relational, 142, 242, 386, 512, 513, 516
partial order, 131, 139, 156, 395, 396
phase transition, 143–145, 176, 183, 198, 415, 416
phenomenology
quantum gravity, 27, 161, 164, 407, 408, 427–432,
436–440, 442, 443, 445, 447, 466, 485, 504,
507, 517, 543, 561
Planck
constant, 493
energy, 108, 178, 199, 304
length, 5, 6, 14, 16, 17, 153, 154, 160, 293, 427,
442, 447, 528, 554
mass, 125, 126, 161, 308, 388, 517, 524
scale, 5–7, 9, 15, 27, 88, 90, 111, 139, 143, 148,
157, 160–163, 178, 181, 231, 249, 274, 327,
394, 400, 410, 419, 427–430, 434, 436–441,
443, 444, 447, 466, 485, 495, 505, 530, 532,
535, 536, 541, 542, 554, 564, 565, 575, 578
time, 16, 387, 578, 579
units, 117, 122, 124, 160, 188, 189, 191, 204, 408,
521
presheaves, 86, 87, 92
projective structures, 50, 52, 57
quantization
asymptotic, 64
canonical, 49, 54, 56, 69, 75, 80, 140, 237, 243,
253, 272, 325, 332, 335, 363, 369, 373, 378,
379, 388, 421, 514, 577
history formalism, 70–72, 79–82
path integral, 46, 50, 56, 63, 71, 91, 140, 181, 230,
254, 268, 269, 272, 274, 275, 286, 292, 311,
316, 323–325, 335, 342–345, 351, 357, 363,
364, 369, 370, 378, 379, 386, 394, 403, 406,
415, 417, 554, 577
perturbative, 69, 111, 162, 236
quantum computation, 102, 104, 136, 146, 165
Quantum Gravity
conceptual difficulties, 8
non-perturbative, 6, 210
perturbative, 13, 14, 64
problem of, 5, 7, 13, 15, 52, 99, 102, 108, 109, 427,
433, 434, 451
quantum liquids, 100–102, 104, 109, 157, 158, 329
quantum states
in holographic theories, 17
of gravitational field, 7, 14, 16, 23, 45
reality conditions, 243, 254, 270, 336
Regge calculus, 104, 124, 137, 139, 293, 318,
322–325, 328, 341, 360–366, 369–374, 379,
385, 386, 400, 420–422
renormalizability, 111, 162, 188, 236, 272, 287, 288,
334, 335, 344, 452, 454, 458, 530, 531, 534
non-, 9, 14, 111, 116, 120, 162, 236, 451, 456–458,
462, 463, 534, 535
perturbative, 115, 116, 123, 125
renormalization, 41, 142, 155, 299, 317, 320, 321,
324, 327, 329, 344, 357, 394, 406, 531–533,
540
simplicial complexes, 85, 87, 88, 90, 95, 96, 104, 156,
311–313, 315, 318, 320, 324, 326, 329, 336,
341, 343, 344, 346, 374, 420, 421
and manifolds, 90
as categories, 88, 90
as nerves of categories, 88
bi-simplicial complexes, 96
simplicial geometry, 322, 323, 327, 351, 361,
369–371, 421
singularity, 555
big bang, 9, 249, 386, 390, 403, 549, 555, 566
black hole, 177, 403, 509, 549, 555, 566
spacetime, 160
atoms of, 152, 571
background, 143, 210, 217, 348
categorical, 95
continuous, 84, 138, 150, 159, 160, 466, 528
diffeomorphisms, 270
dimension, 15, 349, 352, 353, 357, 372, 422, 423,
550, 552, 559
compactified, 16, 22
effective, 141
extra, 4, 5, 169–172, 179, 187, 207, 212, 224,
509
Hausdorff, 141, 142, 151, 152, 156, 343, 422,
423
topological, 155, 156
discreteness, 9, 18, 26–28, 33, 38, 40, 88, 90, 124,
150, 151, 153, 154, 159, 160, 192, 193, 249,
253, 260, 264, 270, 293, 313, 327–329, 391,
393–396, 401, 403, 407, 410, 422, 429, 433,
436, 536, 539, 542, 549, 554, 555, 559, 576,
577