Approaches to Quantum Gravity

More documents

Recommendations

Info

List of contribu<strong>to</strong>rsxiiiW. TaylorMassachusetts Institute of Technology, Lab for Nuclear Science and Center forTheoretical Physics, 77 Massachusetts Ave., Cambridge, MA 02139-4307, USAT. ThiemannMax-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, D-14476 Golm, GermanyandPerimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo N2L2Y5, Ontario, CanadaG. ’t HooftInstitute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CEUtrecht, The NetherlandsR. WilliamsDepartment of Applied Mathematics and Theoretical Physics, Centre forMathematical Sciences, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK
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 34: xviPrefacenew mathematics as well a
Page 38: xviiiPrefaceas the current tentativ
Page 44: Part IFundamental ideas and general
Page 50: 4 C. RovelliQFT relies heavily on g
Page 54: 6 C. RovelliFor instance, the Heise
Page 58: 8 C. RovelliConceptually, the key q
Page 62: 10 C. RovelliIn addition, a number
Page 66: 12 C. Rovelli[20] S. W. Hawking,
Page 70: 14 G. ’t Hooftof time, of Cauchy
Page 74: 16 G. ’t Hooftgenerally, in 2 + 1
Page 78:
18 G. ’t Hooftof the small-distan
Page 82:
20 G. ’t Hooftthat a theory exist
Page 86:
22 G. ’t HooftThis means that the
Page 90:
24 G. ’t Hooft2.7 Gauge- and diff
Page 94:
3Does locality fail at intermediate
Page 98:
28 R. D. Sorkina little thought ind
Page 102:
30 R. D. Sorkinthis approach one no
Page 106:
32 R. D. SorkinThe suggestion of os
Page 110:
34 R. D. SorkinBut is our “discre
Page 114:
36 R. D. Sorkin(as one might have e
Page 118:
38 R. D. SorkinIt seems likely that
Page 122:
40 R. D. Sorkinin particular, would
Page 126:
42 R. D. Sorkinsmall, as discussed
Page 130:
4Prolegomena to any future Quantum
Page 134:
46 J. Stachelbreakups, it is import
Page 138:
48 J. Stachelgauge fields and GR, t
Page 142:
50 J. Stachelwhere S is any 2-surfa
Page 146:
52 J. Stachelconnection (see, e.g.
Page 150:
54 J. Stachelof a projective struct
Page 154:
56 J. Stachelproblem on a spacelike
Page 158:
58 J. Stachel(3) a break-up of the
Page 162:
60 J. Stachelsimplification of the
Page 166:
62 J. Stachelinvestigate (3 + 1) an
Page 170:
64 J. Stachelpartitioned into slice
Page 174:
66 J. Stachel[13] S. Frittelli, C.
Page 178:
5Spacetime symmetries in histories
Page 182:
70 N. Savvidouof time. The developm
Page 186:
72 N. SavvidouIn order to define co
Page 190:
74 N. SavvidouThe novel feature in
Page 194:
76 N. SavvidouWe start instead from
Page 198:
78 N. SavvidouRelation between the
Page 202:
80 N. Savvidou5.4 A spacetime appro
Page 206:
82 N. Savvidouthe T 0 variables - a
Page 210:
Categorical geometry and the mathem
Page 214:
86 L. Cranecalled morphisms [1]. A
Page 218:
88 L. Craneare defined combinatoria
Page 222:
90 L. Crane6.3.1 The BC categorical
Page 226:
92 L. CraneClassical behavior occur
Page 230:
94 L. CraneOne could then apply the
Page 234:
96 L. CraneThis model also has a na
Page 238:
98 L. Crane[13] J. Barrett and L. C
Page 242:
100 O. DreyerIsspacetimefundamental
Page 246:
102 O. DreyerSince the inverse prop
Page 250:
104 O. Dreyerwhere we have denoted
Page 254:
106 O. Dreyerand the points are the
Page 258:
108 O. Dreyerm 1m 2=− v 2v 1. (7.
Page 262:
110 O. DreyerIn addition to the pro
Page 266:
112 R. PercacciIn section 8.2 I int
Page 270:
114 R. Percaccithis case the theory
Page 274:
116 R. PercacciThe requirement of r
Page 278:
118 R. Percaccibe bounded. This is
Page 282:
120 R. Percacciwhere the heat kerne
Page 286:
122 R. Percacci~G10.80.60.40.2-0.2
Page 290:
124 R. Percacciwill still be possib
Page 294:
126 R. PercacciEinstein-Hilbert act
Page 298:
128 R. Percacci[24] O. Lauscher and
Page 302:
130 F. Markopoulouhas been claimed
Page 306:
132 F. Markopoulouvertex x ∈ V (
Page 310:
134 F. MarkopoulouNote that complet
Page 314:
136 F. Markopoulou9.2.2 The meaning
Page 318:
138 F. MarkopoulouFock space for th
Page 322:
140 F. MarkopoulouA = 1A 2A 3A 4===
Page 326:
142 F. Markopouloueffective theorie
Page 330:
144 F. MarkopoulouQuantum Field The
Page 334:
146 F. Markopoulouis concerned with
Page 338:
148 F. MarkopoulouThe dynamics is p
Page 342:
Questions and answers• Q - L. Cra
Page 346:
152 Questions and answersHausdorff
Page 350:
154 Questions and answers- A-R.Sork
Page 354:
156 Questions and answersNow a good
Page 358:
158 Questions and answerswould seem
Page 362:
160 Questions and answers3. You men
Page 366:
162 Questions and answers- A - R. P
Page 370:
164 Questions and answersnotion of
Page 376:
Part IIString/M-theory
Page 382:
170 G. Horowitz and J. Polchinskia
Page 386:
172 G. Horowitz and J. Polchinskiwh
Page 390:
174 G. Horowitz and J. Polchinskiwi
Page 394:
176 G. Horowitz and J. Polchinskiwh
Page 398:
178 G. Horowitz and J. PolchinskiTh
Page 402:
180 G. Horowitz and J. Polchinskimo
Page 406:
182 G. Horowitz and J. PolchinskiNo
Page 410:
184 G. Horowitz and J. Polchinskica
Page 414:
186 G. Horowitz and J. Polchinski[2
Page 418:
188 T. BanksThis looks peculiar to
Page 422:
190 T. BanksThis lightning review o
Page 426:
192 T. BanksSince the holographic s
Page 430:
194 T. Banksdefinition of local evo
Page 434:
196 T. Bankswe have postulated are
Page 438:
198 T. Bankswith observerphilic def
Page 442:
200 T. Banksde Sitter horizon is th
Page 446:
202 T. Banksof the dS-Schwarzschild
Page 450:
204 T. BanksThus, there are of orde
Page 454:
206 T. Banksit has given us a const
Page 458:
208 T. Banks[3] G. T. Horowitz, The
Page 462:
12String field theoryW. TAYLOR12.1
Page 466:
212 W. Taylorpossible configuration
Page 470:
214 W. Taylorraising operators α
Page 474:
216 W. Taylor❍❨ 1❍❍✟✟
Page 478:
218 W. Taylorlevel truncation is to
Page 482:
220 W. Taylordifferent descriptions
Page 486:
222 W. TaylorIn closed string field
Page 490:
224 W. Taylorclosed string field th
Page 494:
226 W. Tayloror other 6D manifold.
Page 498:
228 W. Taylor[37] W. Taylor, & B. Z
Page 502:
230 Questions and answers3. You sta
Page 506:
232 Questions and answers(proving t
Page 512:
13Loop quantum gravityT. THIEMANN13
Page 516:
Loop quantum gravity 23713.2 Canoni
Page 520:
Loop quantum gravity 239In what fol
Page 524:
Loop quantum gravity 241equivalence
Page 528:
Loop quantum gravity 243∂ F τ f,
Page 532:
Loop quantum gravity 245will play t
Page 536:
Loop quantum gravity 247U(ϕ)T n =
Page 540:
Loop quantum gravity 249a definite,
Page 544:
Loop quantum gravity 251[28] T. Thi
Page 548:
14Covariant loop quantum gravity?E.
Page 552:
Covariant loop quantum gravity? 255
Page 556:
Page 560:
Page 564:
Page 568:
Page 572:
Page 576:
Page 580:
Page 584:
Page 588:
The spin foam representation of loo
Page 592:
Page 596:
Page 600:
Page 604:
Page 608:
Page 612:
Page 616:
Page 620:
Page 624:
Three-dimensional spin foam Quantum
Page 628:
Page 632:
Page 636:
Page 640:
Page 644:
Page 648:
Page 652:
Page 656:
Page 660:
Page 664:
The group field theory approach to
Page 668:
Page 672:
Page 676:
Page 680:
Page 684:
Page 688:
Page 692:
Page 696:
Page 700:
Page 704:
Page 708:
Questions and answers 333the holes
Page 712:
Questions and answers 335their vacu
Page 716:
Questions and answers 337of some so
Page 724:
18Quantum Gravity: the art of build
Page 728:
Quantum Gravity: the art of buildin
Page 732:
Page 736:
Page 740:
Page 744:
Page 748:
Page 752:
Page 756:
Page 760:
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?