Approaches to Quantum Gravity

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viiiContents11 String theory, holography and Quantum Gravity 187T. Banks12 String field theory 210W. TaylorQuestions and answers 229Part III Loop quantum gravity and spin foam models 23313 Loop quantum gravity 235T. Thiemann14 Covariant loop quantum gravity? 253E. Livine15 The spin foam representation of loop quantum gravity 272A. Perez16 Three-dimensional spin foam Quantum Gravity 290L. Freidel17 The group field theory approach to Quantum Gravity 310D. OritiQuestions and answers 332Part IV Discrete Quantum Gravity 33918 Quantum Gravity: the art of building spacetime 341J. Ambjørn, J. Jurkiewicz and R. Loll19 Quantum Regge calculus 360R. Williams20 Consistent discretizations as a road to Quantum Gravity 378R. Gambini and J. Pullin21 The causal set approach to Quantum Gravity 393J. HensonQuestions and answers 414Part V Effective models and Quantum Gravity phenomenology 42522 Quantum Gravity phenomenology 427G. Amelino-Camelia23 Quantum Gravity and precision tests 450C. Burgess24 Algebraic approach to Quantum Gravity II: noncommutativespacetime 466S. Majid
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Page 8: APPROACHES TO QUANTUM GRAVITYToward
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Page 20: Contentsix25 Doubly special relativ
Page 24: List of contributorsxiO. DreyerTheo
Page 28: List of contributorsxiiiW. TaylorMa
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,
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14 G. ’t Hooftof time, of Cauchy
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16 G. ’t Hooftgenerally, in 2 + 1
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18 G. ’t Hooftof the small-distan
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20 G. ’t Hooftthat a theory exist
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22 G. ’t HooftThis means that the
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24 G. ’t Hooft2.7 Gauge- and diff
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3Does locality fail at intermediate
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28 R. D. Sorkina little thought ind
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30 R. D. Sorkinthis approach one no
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32 R. D. SorkinThe suggestion of os
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34 R. D. SorkinBut is our “discre
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36 R. D. Sorkin(as one might have e
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38 R. D. SorkinIt seems likely that
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40 R. D. Sorkinin particular, would
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42 R. D. Sorkinsmall, as discussed
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4Prolegomena to any future Quantum
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46 J. Stachelbreakups, it is import
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48 J. Stachelgauge fields and GR, t
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50 J. Stachelwhere S is any 2-surfa
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52 J. Stachelconnection (see, e.g.
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54 J. Stachelof a projective struct
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56 J. Stachelproblem on a spacelike
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58 J. Stachel(3) a break-up of the
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60 J. Stachelsimplification of the
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62 J. Stachelinvestigate (3 + 1) an
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64 J. Stachelpartitioned into slice
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66 J. Stachel[13] S. Frittelli, C.
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5Spacetime symmetries in histories
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70 N. Savvidouof time. The developm
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72 N. SavvidouIn order to define co
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74 N. SavvidouThe novel feature in
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76 N. SavvidouWe start instead from
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78 N. SavvidouRelation between the
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80 N. Savvidou5.4 A spacetime appro
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82 N. Savvidouthe T 0 variables - a
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Categorical geometry and the mathem
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86 L. Cranecalled morphisms [1]. A
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88 L. Craneare defined combinatoria
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90 L. Crane6.3.1 The BC categorical
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92 L. CraneClassical behavior occur
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94 L. CraneOne could then apply the
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96 L. CraneThis model also has a na
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98 L. Crane[13] J. Barrett and L. C
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100 O. DreyerIsspacetimefundamental
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102 O. DreyerSince the inverse prop
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104 O. Dreyerwhere we have denoted
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106 O. Dreyerand the points are the
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108 O. Dreyerm 1m 2=− v 2v 1. (7.
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110 O. DreyerIn addition to the pro
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112 R. PercacciIn section 8.2 I int
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114 R. Percaccithis case the theory
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116 R. PercacciThe requirement of r
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118 R. Percaccibe bounded. This is
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120 R. Percacciwhere the heat kerne
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122 R. Percacci~G10.80.60.40.2-0.2
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124 R. Percacciwill still be possib
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126 R. PercacciEinstein-Hilbert act
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128 R. Percacci[24] O. Lauscher and
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130 F. Markopoulouhas been claimed
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132 F. Markopoulouvertex x ∈ V (
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134 F. MarkopoulouNote that complet
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136 F. Markopoulou9.2.2 The meaning
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138 F. MarkopoulouFock space for th
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140 F. MarkopoulouA = 1A 2A 3A 4===
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142 F. Markopouloueffective theorie
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144 F. MarkopoulouQuantum Field The
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146 F. Markopoulouis concerned with
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148 F. MarkopoulouThe dynamics is p
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Questions and answers• Q - L. Cra
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152 Questions and answersHausdorff
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154 Questions and answers- A-R.Sork
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156 Questions and answersNow a good
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158 Questions and answerswould seem
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160 Questions and answers3. You men
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162 Questions and answers- A - R. P
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164 Questions and answersnotion of
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Part IIString/M-theory
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170 G. Horowitz and J. Polchinskia
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172 G. Horowitz and J. Polchinskiwh
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174 G. Horowitz and J. Polchinskiwi
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176 G. Horowitz and J. Polchinskiwh
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178 G. Horowitz and J. PolchinskiTh
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180 G. Horowitz and J. Polchinskimo
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182 G. Horowitz and J. PolchinskiNo
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184 G. Horowitz and J. Polchinskica
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186 G. Horowitz and J. Polchinski[2
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188 T. BanksThis looks peculiar to
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190 T. BanksThis lightning review o
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192 T. BanksSince the holographic s
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194 T. Banksdefinition of local evo
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196 T. Bankswe have postulated are
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198 T. Bankswith observerphilic def
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200 T. Banksde Sitter horizon is th
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202 T. Banksof the dS-Schwarzschild
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204 T. BanksThus, there are of orde
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206 T. Banksit has given us a const
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208 T. Banks[3] G. T. Horowitz, The
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12String field theoryW. TAYLOR12.1
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212 W. Taylorpossible configuration
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214 W. Taylorraising operators α
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216 W. Taylor❍❨ 1❍❍✟✟
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218 W. Taylorlevel truncation is to
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220 W. Taylordifferent descriptions
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222 W. TaylorIn closed string field
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224 W. Taylorclosed string field th
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226 W. Tayloror other 6D manifold.
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228 W. Taylor[37] W. Taylor, & B. Z
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230 Questions and answers3. You sta
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232 Questions and answers(proving t
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13Loop quantum gravityT. THIEMANN13
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Loop quantum gravity 23713.2 Canoni
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Loop quantum gravity 239In what fol
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Loop quantum gravity 241equivalence
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Loop quantum gravity 243∂ F τ f,
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Loop quantum gravity 245will play t
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Loop quantum gravity 247U(ϕ)T n =
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Loop quantum gravity 249a definite,
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Loop quantum gravity 251[28] T. Thi
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14Covariant loop quantum gravity?E.
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Covariant loop quantum gravity? 255
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The spin foam representation of loo
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Three-dimensional spin foam Quantum
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The group field theory approach to
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Questions and answers 333the holes
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Questions and answers 335their vacu
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Questions and answers 337of some so
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18Quantum Gravity: the art of build
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Quantum Gravity: the art of buildin
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Quantum Regge calculus 361is given
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Quantum Regge calculus 363group. We
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Quantum Regge calculus 365emanating
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Quantum Regge calculus 367We will s
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Quantum Regge calculus 369reason, d
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Quantum Regge calculus 371gravitati
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Quantum Regge calculus 373where ξ
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Quantum Regge calculus 375[4] J. W.
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Quantum Regge calculus 377[52] M. L
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Consistent discretizations as a roa
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21The causal set approach to Quantu
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The causal set approach to Quantum
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22Quantum Gravity phenomenologyG. A
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Quantum Gravity phenomenology 429Ta
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Quantum Gravity phenomenology 431th
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Quantum Gravity phenomenology 433co
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Quantum Gravity phenomenology 435po
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Quantum Gravity phenomenology 437Fr
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Quantum Gravity phenomenology 439le
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Quantum Gravity phenomenology 441pr
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Quantum Gravity phenomenology 443wa
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Quantum Gravity phenomenology 445is
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Quantum Gravity phenomenology 447sc
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Quantum Gravity phenomenology 449[2
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Quantum Gravity and precision tests
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Algebraic approach to Quantum Gravi
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25Doubly special relativityJ. KOWAL
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Doubly special relativity 495DSR to
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Doubly special relativity 497On the
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Doubly special relativity 499some o
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Doubly special relativity 501[x 0 ,
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Doubly special relativity 503that t
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Doubly special relativity 505can be
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Doubly special relativity 507scale,
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26From quantum reference frames to
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From quantum reference frames to de
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Lorentz invariance violation & its
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Generic predictions of quantum theo
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Questions and answers• Q - L. Cra
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Questions and answers 573frame. Jus
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Questions and answers 575- A - J. K
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Questions and answers 577where this
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Questions and answers 579would allo
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Index 581cosmology, 26, 155, 184, 1
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Index 583emergent, 99, 109, 163, 17
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Approaches to Quantum Gravity

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