Approaches to Quantum Gravity

More documents

Recommendations

Info

Part V Effective models and <strong>Quantum</strong> <strong>Gravity</strong> phenomenology
Page 2:
This page intentionally left blank
Page 8:
APPROACHES TO QUANTUM GRAVITY Towar
Page 12:
A Sandra
Page 18:
viii Contents 11 String theory, hol
Page 22:
Contributors J. Ambjørn The Niels
Page 26:
xii List of contributors D. Oriti M
Page 32:
Preface Quantum Gravity is a dream,
Page 36:
Preface xvii are following in their
Page 40:
Preface xix enormous amount of prog
Page 48:
1 Unfinished revolution C. ROVELLI
Page 52:
Unfinished revolution 5 wit of empi
Page 56:
Unfinished revolution 7 In general
Page 60:
Unfinished revolution 9 However, re
Page 64:
Unfinished revolution 11 References
Page 68:
2 The fundamental nature of space a
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 intermedi
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:
7 Emergent relativity O. DREYER 7.1
Page 244:
A (a) Emergent relativity 101 (b) (
Page 248:
Emergent relativity 103 It is here
Page 252:
Emergent relativity 105 spacetime c
Page 256:
Emergent relativity 107 φ A B Fig.
Page 260:
Emergent relativity 109 If, on the
Page 264:
8 Asymptotic safety R. PERCACCI 8.1
Page 268:
Asymptotic safety 113 field and the
Page 272:
Asymptotic safety 115 For example,
Page 276:
Asymptotic safety 117 If we choose
Page 280:
Asymptotic safety 119 complex field
Page 284:
Asymptotic safety 121 2 G ~ ~ 1.5 1
Page 288:
Asymptotic safety 123 larger, and i
Page 292:
Asymptotic safety 125 Dimensional a
Page 296:
Asymptotic safety 127 References [1
Page 300:
9 New directions in background inde
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 151 Quantum G
Page 348:
Questions and answers 153 was that
Page 352:
Questions and answers 155 causality
Page 356:
Questions and answers 157 to hold),
Page 360:
Questions and answers 159 of how gr
Page 364:
Questions and answers 161 the actio
Page 368:
Questions and answers 163 allow us
Page 372:
Questions and answers 165 - A-F.Mar
Page 380:
10 Gauge/gravity duality G. HOROWIT
Page 384:
Gauge/gravity duality 171 strong an
Page 388:
Gauge/gravity duality 173 decompose
Page 392:
Gauge/gravity duality 175 Here l s
Page 396:
Gauge/gravity duality 177 There is
Page 400:
Gauge/gravity duality 179 these are
Page 404:
Gauge/gravity duality 181 leading t
Page 408:
Gauge/gravity duality 183 states to
Page 412:
Gauge/gravity duality 185 [6] N. Be
Page 416:
11 String theory, holography and Qu
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 211 no tools to
Page 468:
String field theory 213 made an ins
Page 472:
(d) Cyclicity: ∫ ⋆= (−1) G G
Page 476:
String field theory 217 however, th
Page 480:
String field theory 219 12.2.3 Outs
Page 484:
String field theory 221 a review) g
Page 488:
String field theory 223 similar com
Page 492:
String field theory 225 this; the p
Page 496:
String field theory 227 [11] T. G.
Page 500:
Questions and answers • Q - D. Or
Page 504:
Questions and answers 231 condition
Page 508:
Part III Loop quantum gravity and s
Page 514:
236 T. Thiemann (anti)commute. We s
Page 518:
238 T. Thiemann Notice that in gene
Page 522:
240 T. Thiemann spectrum of all the
Page 526:
242 T. Thiemann order to avoid anom
Page 530:
244 T. Thiemann We consider spaceti
Page 534:
246 T. Thiemann Hence both gauge gr
Page 538:
248 T. Thiemann that Ĉ(N) cannot b
Page 542:
250 T. Thiemann [8] R. Brunetti, K.
Page 546:
252 T. Thiemann [48] M. Bojowald, H
Page 550:
254 E. Livine SU(2) gauge theory. T
Page 554:
256 E. Livine space; η IJ is the f
Page 558:
258 E. Livine However, in contrast
Page 562:
260 E. Livine (i) Either we work wi
Page 566:
262 E. Livine At the end of the day
Page 570:
264 E. Livine projector at the end
Page 574:
266 E. Livine for a surface S inter
Page 578:
268 E. Livine This constraint is sa
Page 582:
270 E. Livine we do not need the se
Page 586:
15 The spin foam representation of
Page 590:
274 A. Perez in classical general r
Page 594:
276 A. Perez where M = ×R (for an
Page 598:
278 A. Perez the Levi-Civita tensor
Page 602:
280 A. Perez k Tr[ k (W p )] ✄ j
Page 606:
282 A. Perez j j j k j k m k m j j
Page 610:
284 A. Perez Here we studied the in
Page 614:
286 A. Perez A spin foam representa
Page 618:
288 A. Perez master-constraint prog
Page 622:
16 Three-dimensional spin foam Quan
Page 626:
292 L. Freidel 16.3 The Ponzano-Reg
Page 630:
294 L. Freidel under usual gauge tr
Page 634:
296 L. Freidel is now constrained t
Page 638:
298 L. Freidel 16.4.1 Mathematical
Page 642:
300 L. Freidel Therefore, at first
Page 646:
302 L. Freidel The inverse group Fo
Page 650:
304 L. Freidel From this identity,
Page 654:
306 L. Freidel choice of statistics
Page 658:
308 L. Freidel A deeper study of th
Page 662:
17 The group field theory approach
Page 666:
312 D. Oriti simplicial complex, or
Page 670:
314 D. Oriti are not all simultaneo
Page 674:
316 D. Oriti diagrams correspond to
Page 678:
318 D. Oriti is the simple fact tha
Page 682:
320 D. Oriti better, by a single ma
Page 686:
322 D. Oriti or SO(3, 1)) [8; 9; 10
Page 690:
324 D. Oriti where: g i ∈ G, s i
Page 694:
326 D. Oriti observables in GFTs ar
Page 698:
328 D. Oriti research. On the other
Page 702:
330 D. Oriti of the possibility of
Page 706:
Questions and answers • Q - L. Cr
Page 710:
334 Questions and answers I partly
Page 714:
336 Questions and answers spectrum
Page 720:
Part IV Discrete Quantum Gravity
Page 726:
342 J. Ambjørn, J. Jurkiewicz and
Page 730:
Page 734:
Page 738:
Page 742:
Page 746:
Page 750:
Page 754:
Page 758:
Page 762:
19 Quantum Regge calculus R. WILLIA
Page 766:
362 R. Williams only in flat space
Page 770:
364 R. Williams where V is the volu
Page 774:
366 R. Williams equations of motion
Page 778:
368 R. Williams Dropping the 1/d co
Page 782:
370 R. Williams At a typical interi
Page 786:
372 R. Williams about which it make
Page 790:
374 R. Williams dealt with include
Page 794:
376 R. Williams [27] H. W. Hamber,
Page 798:
20 Consistent discretizations as a
Page 802:
380 R. Gambini and J. Pullin The mo
Page 806:
382 R. Gambini and J. Pullin phase
Page 810:
384 R. Gambini and J. Pullin 2 1 q
Page 814:
386 R. Gambini and J. Pullin of the
Page 818:
388 R. Gambini and J. Pullin accept
Page 822:
390 R. Gambini and J. Pullin isomor
Page 826:
392 R. Gambini and J. Pullin [3] C.
Page 830:
394 J. Henson all the other subject
Page 834:
396 J. Henson z y x Fig. 21.1. A ca
Page 838: 398 J. Henson this way, no discrete
Page 842: 400 J. Henson out various sprinklin
Page 846: 402 J. Henson commutes with rotatio
Page 850: 404 J. Henson black hole entropy (o
Page 854: 406 J. Henson “Kleitman-Rothschil
Page 858: 408 J. Henson histories suggest any
Page 862: 410 J. Henson the type normally use
Page 866: 412 J. Henson [17] R. D. Sorkin (19
Page 870: Questions and answers • Q - J. He
Page 874: 416 Questions and answers that the
Page 878: 418 Questions and answers 2. The ab
Page 882: 420 Questions and answers not unimp
Page 886: 422 Questions and answers - A - R.
Page 896: 22 Quantum Gravity phenomenology G.
Page 900: Quantum Gravity phenomenology 429 T
Page 904: Quantum Gravity phenomenology 431 t
Page 908: Quantum Gravity phenomenology 433 c
Page 912: Quantum Gravity phenomenology 435 p
Page 916: Quantum Gravity phenomenology 437 F
Page 920: Quantum Gravity phenomenology 439 l
Page 924: Quantum Gravity phenomenology 441 p
Page 928: Quantum Gravity phenomenology 443 w
Page 932: Quantum Gravity phenomenology 445 i
Page 936: Quantum Gravity phenomenology 447 s
Page 940:
Quantum Gravity phenomenology 449 [
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:
25 Doubly special relativity J. KOW
Page 1032:
Doubly special relativity 495 DSR t
Page 1036:
Doubly special relativity 497 On th
Page 1040:
Doubly special relativity 499 some
Page 1044:
Doubly special relativity 501 [x 0
Page 1048:
Doubly special relativity 503 that
Page 1052:
Doubly special relativity 505 can b
Page 1056:
Doubly special relativity 507 scale
Page 1060:
26 From 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. Cr
Page 1188:
Questions and answers 573 frame. Ju
Page 1192:
Questions and answers 575 - A - J.
Page 1196:
Questions and answers 577 where thi
Page 1200:
Questions and answers 579 would all
Page 1204:
Index 581 cosmology, 26, 155, 184,
Page 1208:
Index 583 emergent, 99, 109, 163, 1
show all

Approaches to Quantum Gravity

Create successful ePaper yourself

Delete template?

Save as template?