Approaches to Quantum Gravity

More documents

Recommendations

Info

354 J. Ambjørn, J. Jurkiewicz and R. Lollway. We therefore make a general ansatz for the probability distribution for largeV 3 (t) as[exp − c ( ) ]1 dV3 (t) 2− c 2 V3 αV 3 (t) dt(t) , (18.26)where 0 ≤ α
Page 2:
This page intentionally left blank
Page 8:
APPROACHES TO QUANTUM GRAVITYToward
Page 12:
A Sandra
Page 18:
viiiContents11 String theory, holog
Page 22:
ContributorsJ. AmbjørnThe Niels Bo
Page 26:
xiiList of contributorsD. OritiMax
Page 32:
PrefaceQuantum Gravity is a dream,
Page 36:
Prefacexviiare following in their s
Page 40:
Prefacexixenormous amount of progre
Page 48:
1Unfinished revolutionC. ROVELLIOne
Page 52:
Unfinished revolution 5wit of empir
Page 56:
Unfinished revolution 7In general r
Page 60:
Unfinished revolution 9However, res
Page 64:
Unfinished revolution 11References[
Page 68:
2The fundamental nature of space an
Page 72:
The fundamental nature of space and
Page 76:
Page 80:
Page 84:
Page 88:
Page 92:
Page 96:
Does locality fail at intermediate
Page 100:
Page 104:
Page 108:
Page 112:
Page 116:
∫Does locality fail at intermedia
Page 120:
Page 124:
Page 128:
Page 132:
Prolegomena to any future Quantum G
Page 136:
Page 140:
Page 144:
Page 148:
Page 152:
Page 156:
Page 160:
Page 164:
Page 168:
Page 172:
Page 176:
Page 180:
Spacetime symmetries in histories c
Page 184:
Page 188:
Page 192:
Page 196:
Page 200:
Page 204:
Page 208:
Page 212:
Categorical geometry and the mathem
Page 216:
Page 220:
Page 224:
Page 228:
Page 232:
Page 236:
Page 240:
7Emergent relativityO. DREYER7.1 In
Page 244:
A(a)Emergent relativity 101(b)(c)B(
Page 248:
Emergent relativity 103It is here t
Page 252:
Emergent relativity 105spacetime co
Page 256:
Emergent relativity 107φABFig. 7.4
Page 260:
Emergent relativity 109If, on the o
Page 264:
8Asymptotic safetyR. PERCACCI8.1 In
Page 268:
Asymptotic safety 113field and the
Page 272:
Asymptotic safety 115For example, t
Page 276:
Asymptotic safety 117If we choose k
Page 280:
Asymptotic safety 119complex fields
Page 284:
Asymptotic safety 1212G ~ ~1.510.5-
Page 288:
Asymptotic safety 123larger, and it
Page 292:
Asymptotic safety 125Dimensional an
Page 296:
Asymptotic safety 127References[1]
Page 300:
9New directions in background indep
Page 304:
New directions in background indepe
Page 308:
Page 312:
Page 316:
Page 320:
Page 324:
Page 328:
Page 332:
Page 336:
Page 340:
Page 344:
Questions and answers 151Quantum Gr
Page 348:
Questions and answers 153was that t
Page 352:
Questions and answers 155causality
Page 356:
Questions and answers 157to hold),
Page 360:
Questions and answers 159of how gra
Page 364:
Questions and answers 161the action
Page 368:
Questions and answers 163allow us t
Page 372:
Questions and answers 165- A-F.Mark
Page 380:
10Gauge/gravity dualityG. HOROWITZ
Page 384:
Gauge/gravity duality 171strong and
Page 388:
Gauge/gravity duality 173decomposed
Page 392:
Gauge/gravity duality 175Here l s i
Page 396:
Gauge/gravity duality 177There is a
Page 400:
Gauge/gravity duality 179these are
Page 404:
Gauge/gravity duality 181leading to
Page 408:
Gauge/gravity duality 183states to
Page 412:
Gauge/gravity duality 185[6] N. Ber
Page 416:
11String theory, holography and Qua
Page 420:
String theory, holography and Quant
Page 424:
Page 428:
Page 432:
Page 436:
Page 440:
Page 444:
Page 448:
Page 452:
Page 456:
Page 460:
Page 464:
String field theory 211no tools to
Page 468:
String field theory 213made an insi
Page 472:
(d) Cyclicity: ∫ ⋆= (−1) G G
Page 476:
String field theory 217however, the
Page 480:
String field theory 21912.2.3 Outst
Page 484:
String field theory 221a review) gi
Page 488:
String field theory 223similar comp
Page 492:
String field theory 225this; the ph
Page 496:
String field theory 227[11] T. G. E
Page 500:
Questions and answers• Q - D. Ori
Page 504:
Questions and answers 231condition
Page 508:
Part IIILoop quantum gravity and sp
Page 514:
236 T. Thiemann(anti)commute. We se
Page 518:
238 T. ThiemannNotice that in gener
Page 522:
240 T. Thiemannspectrum of all the
Page 526:
242 T. Thiemannorder to avoid anoma
Page 530:
244 T. ThiemannWe consider spacetim
Page 534:
246 T. ThiemannHence both gauge gro
Page 538:
248 T. Thiemannthat Ĉ(N) cannot be
Page 542:
250 T. Thiemann[8] R. Brunetti, K.
Page 546:
252 T. Thiemann[48] M. Bojowald, H.
Page 550:
254 E. LivineSU(2) gauge theory. Th
Page 554:
256 E. Livinespace; η IJ is the fl
Page 558:
258 E. LivineHowever, in contrast t
Page 562:
260 E. Livine(i) Either we work wit
Page 566:
262 E. LivineAt the end of the day,
Page 570:
264 E. Livineprojector at the end v
Page 574:
266 E. Livinefor a surface S inters
Page 578:
268 E. LivineThis constraint is sat
Page 582:
270 E. Livinewe do not need the sec
Page 586:
15The spin foam representation of l
Page 590:
274 A. Perezin classical general re
Page 594:
276 A. Perezwhere M = ×R (for an
Page 598:
278 A. Perezthe Levi-Civita tensor.
Page 602:
280 A. PerezkTr[ k (W p )] ✄jP=
Page 606:
282 A. Perezjjjkjkmkmjjjjmkmkmkmkkj
Page 610:
284 A. PerezHere we studied the int
Page 614:
286 A. PerezA spin foam representat
Page 618:
288 A. Perezmaster-constraint progr
Page 622:
16Three-dimensional spin foam Quant
Page 626:
292 L. Freidel16.3 The Ponzano-Regg
Page 630:
294 L. Freidelunder usual gauge tra
Page 634:
296 L. Freidelis now constrained to
Page 638:
298 L. Freidel16.4.1 Mathematical s
Page 642:
300 L. FreidelTherefore, at first o
Page 646:
302 L. FreidelThe inverse group Fou
Page 650:
304 L. FreidelFrom this identity, i
Page 654:
306 L. Freidelchoice of statistics.
Page 658:
308 L. FreidelA deeper study of the
Page 662:
17The group field theory approach t
Page 666:
312 D. Oritisimplicial complex, or
Page 670:
314 D. Oritiare not all simultaneou
Page 674:
316 D. Oritidiagrams correspond to
Page 678:
318 D. Oritiis the simple fact that
Page 682:
320 D. Oritibetter, by a single mat
Page 686:
322 D. Oritior SO(3, 1)) [8; 9; 10]
Page 690:
324 D. Oritiwhere: g i ∈ G, s i
Page 694:
326 D. Oritiobservables in GFTs are
Page 698: 328 D. Oritiresearch. On the other
Page 702: 330 D. Oritiof the possibility of a
Page 706: Questions and answers• Q - L. Cra
Page 710: 334 Questions and answersI partly d
Page 714: 336 Questions and answersspectrum i
Page 720: Part IVDiscrete Quantum Gravity
Page 726: 342 J. Ambjørn, J. Jurkiewicz and
Page 752: Quantum Gravity: the art of buildin
Page 764: Quantum Regge calculus 361is given
Page 768: Quantum Regge calculus 363group. We
Page 772: Quantum Regge calculus 365emanating
Page 776: Quantum Regge calculus 367We will s
Page 780: Quantum Regge calculus 369reason, d
Page 784: Quantum Regge calculus 371gravitati
Page 788: Quantum Regge calculus 373where ξ
Page 792: Quantum Regge calculus 375[4] J. W.
Page 796: Quantum Regge calculus 377[52] M. L
Page 800:
Consistent discretizations as a roa
Page 804:
Page 808:
Page 812:
Page 816:
Page 820:
Page 824:
Page 828:
21The causal set approach to Quantu
Page 832:
The causal set approach to Quantum
Page 836:
Page 840:
Page 844:
Page 848:
Page 852:
Page 856:
Page 860:
Page 864:
Page 868:
Page 872:
Page 876:
Page 880:
Page 884:
Page 888:
Page 896:
22Quantum Gravity phenomenologyG. A
Page 900:
Quantum Gravity phenomenology 429Ta
Page 904:
Quantum Gravity phenomenology 431th
Page 908:
Quantum Gravity phenomenology 433co
Page 912:
Quantum Gravity phenomenology 435po
Page 916:
Quantum Gravity phenomenology 437Fr
Page 920:
Quantum Gravity phenomenology 439le
Page 924:
Quantum Gravity phenomenology 441pr
Page 928:
Quantum Gravity phenomenology 443wa
Page 932:
Quantum Gravity phenomenology 445is
Page 936:
Quantum Gravity phenomenology 447sc
Page 940:
Quantum Gravity phenomenology 449[2
Page 944:
Quantum Gravity and precision tests
Page 948:
Page 952:
Page 956:
Page 960:
Page 964:
Page 968:
Page 972:
Page 976:
Algebraic approach to Quantum Gravi
Page 980:
Page 984:
Page 988:
Page 992:
Page 996:
Page 1000:
Page 1004:
Page 1008:
Page 1012:
Page 1016:
Page 1020:
Page 1024:
Page 1028:
25Doubly special relativityJ. KOWAL
Page 1032:
Doubly special relativity 495DSR to
Page 1036:
Doubly special relativity 497On the
Page 1040:
Doubly special relativity 499some o
Page 1044:
Doubly special relativity 501[x 0 ,
Page 1048:
Doubly special relativity 503that t
Page 1052:
Doubly special relativity 505can be
Page 1056:
Doubly special relativity 507scale,
Page 1060:
26From quantum reference frames to
Page 1064:
From quantum reference frames to de
Page 1068:
Page 1072:
Page 1076:
Page 1080:
Page 1084:
Page 1088:
Page 1092:
Page 1096:
Page 1100:
Lorentz invariance violation & its
Page 1104:
Page 1108:
Page 1112:
Page 1116:
Page 1120:
Page 1124:
Page 1128:
Page 1132:
Page 1136:
Page 1140:
Generic predictions of quantum theo
Page 1144:
Page 1148:
Page 1152:
Page 1156:
Page 1160:
Page 1164:
Page 1168:
Page 1172:
Page 1176:
Page 1180:
Page 1184:
Questions and answers• Q - L. Cra
Page 1188:
Questions and answers 573frame. Jus
Page 1192:
Questions and answers 575- A - J. K
Page 1196:
Questions and answers 577where this
Page 1200:
Questions and answers 579would allo
Page 1204:
Index 581cosmology, 26, 155, 184, 1
Page 1208:
Index 583emergent, 99, 109, 163, 17
show all

Approaches to Quantum Gravity

Create successful ePaper yourself

Delete template?

Save as template?