Approaches to Quantum Gravity

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APPROACHES TO QUANTUM GRAVITYToward a New Understanding of Space,Time and MatterEdited byDANIELE ORITIMax Planck Institute for Gravitational Physics,Potsdam, Germany
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Page 10: CAMBRIDGE UNIVERSITY PRESSCambridge
Page 16: ContentsList of contributorsPreface
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
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8 C. RovelliConceptually, the key q
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10 C. RovelliIn addition, a number
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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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