Approaches to Quantum Gravity

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List of contribu<strong>to</strong>rs xiii W. Taylor Massachusetts Institute of Technology, Lab for Nuclear Science and Center for Theoretical Physics, 77 Massachusetts Ave., Cambridge, MA 02139-4307, USA T. Thiemann Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany and Perimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo N2L 2Y5, Ontario, Canada G. ’t Hooft Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands R. Williams Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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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 34: xvi Preface new mathematics as well
Page 38: xviii Preface as the current tentat
Page 44: Part I Fundamental ideas and genera
Page 50: 4 C. Rovelli QFT relies heavily on
Page 54: 6 C. Rovelli For instance, the Heis
Page 58: 8 C. Rovelli Conceptually, the key
Page 62: 10 C. Rovelli In addition, a number
Page 66: 12 C. Rovelli [20] S. W. Hawking,
Page 70: 14 G. ’t Hooft of time, of Cauchy
Page 74: 16 G. ’t Hooft generally, in 2 +
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18 G. ’t Hooft of the small-dista
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20 G. ’t Hooft that a theory exis
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22 G. ’t Hooft This means that th
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24 G. ’t Hooft 2.7 Gauge- and dif
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3 Does locality fail at intermediat
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28 R. D. Sorkin a little thought in
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30 R. D. Sorkin this approach one n
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32 R. D. Sorkin The suggestion of o
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34 R. D. Sorkin But is our “discr
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36 R. D. Sorkin (as one might have
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38 R. D. Sorkin It seems likely tha
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40 R. D. Sorkin in particular, woul
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42 R. D. Sorkin small, as discussed
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4 Prolegomena to any future Quantum
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46 J. Stachel breakups, it is impor
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48 J. Stachel gauge fields and GR,
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50 J. Stachel where S is any 2-surf
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52 J. Stachel connection (see, e.g.
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54 J. Stachel of a projective struc
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56 J. Stachel problem on a spacelik
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58 J. Stachel (3) a break-up of the
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60 J. Stachel simplification of the
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62 J. Stachel investigate (3 + 1) a
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64 J. Stachel partitioned into slic
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66 J. Stachel [13] S. Frittelli, C.
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5 Spacetime symmetries in histories
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70 N. Savvidou of time. The develop
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72 N. Savvidou In order to define c
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74 N. Savvidou The novel feature in
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76 N. Savvidou We start instead fro
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78 N. Savvidou Relation between the
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80 N. Savvidou 5.4 A spacetime appr
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82 N. Savvidou the T 0 variables -
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Categorical geometry and the mathem
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86 L. Crane called morphisms [1]. A
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88 L. Crane are defined combinatori
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90 L. Crane 6.3.1 The BC categorica
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92 L. Crane Classical behavior occu
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94 L. Crane One could then apply th
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96 L. Crane This model also has a n
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98 L. Crane [13] J. Barrett and L.
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100 O. Dreyer Is spacetime fundamen
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102 O. Dreyer Since the inverse pro
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104 O. Dreyer where we have denoted
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106 O. Dreyer and the points are th
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108 O. Dreyer m 1 m 2 =− v 2 v 1
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110 O. Dreyer In addition to the pr
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112 R. Percacci In section 8.2 I in
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114 R. Percacci this case the theor
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116 R. Percacci The requirement of
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118 R. Percacci be bounded. This is
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120 R. Percacci where the heat kern
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122 R. Percacci ~ G 1 0.8 0.6 0.4 0
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124 R. Percacci will still be possi
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126 R. Percacci Einstein-Hilbert ac
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128 R. Percacci [24] O. Lauscher an
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130 F. Markopoulou has been claimed
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132 F. Markopoulou vertex x ∈ V (
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134 F. Markopoulou Note that comple
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136 F. Markopoulou 9.2.2 The meanin
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138 F. Markopoulou Fock space for t
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140 F. Markopoulou A = 1 A 2 A 3 A
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142 F. Markopoulou effective theori
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144 F. Markopoulou Quantum Field Th
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146 F. Markopoulou is concerned wit
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148 F. Markopoulou The dynamics is
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Questions and answers • Q - L. Cr
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152 Questions and answers Hausdorff
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154 Questions and answers - A-R.Sor
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156 Questions and answers Now a goo
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158 Questions and answers would see
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160 Questions and answers 3. You me
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162 Questions and answers - A - R.
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164 Questions and answers notion of
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Part II String/M-theory
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170 G. Horowitz and J. Polchinski a
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172 G. Horowitz and J. Polchinski w
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178 G. Horowitz and J. Polchinski T
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180 G. Horowitz and J. Polchinski m
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182 G. Horowitz and J. Polchinski N
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184 G. Horowitz and J. Polchinski c
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186 G. Horowitz and J. Polchinski [
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188 T. Banks This looks peculiar to
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190 T. Banks This lightning review
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192 T. Banks Since the holographic
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194 T. Banks definition of local ev
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196 T. Banks we have postulated are
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198 T. Banks with observerphilic de
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200 T. Banks de Sitter horizon is t
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202 T. Banks of the dS-Schwarzschil
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204 T. Banks Thus, there are of ord
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206 T. Banks it has given us a cons
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208 T. Banks [3] G. T. Horowitz, Th
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12 String field theory W. TAYLOR 12
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212 W. Taylor possible configuratio
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214 W. Taylor raising operators α
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216 W. Taylor ❍❨ 1 ❍❍✟
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218 W. Taylor level truncation is t
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220 W. Taylor different description
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222 W. Taylor In closed string fiel
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224 W. Taylor closed string field t
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226 W. Taylor or other 6D manifold.
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228 W. Taylor [37] W. Taylor, & B.
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230 Questions and answers 3. You st
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232 Questions and answers (proving
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13 Loop quantum gravity T. THIEMANN
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Loop quantum gravity 237 13.2 Canon
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Loop quantum gravity 239 In what fo
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Loop quantum gravity 241 equivalenc
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Loop quantum gravity 243 ∂ F τ f
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Loop quantum gravity 245 will play
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Loop quantum gravity 247 U(ϕ)T n =
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Loop quantum gravity 249 a definite
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Loop quantum gravity 251 [28] T. Th
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14 Covariant loop quantum gravity?
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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 333 the holes
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Questions and answers 335 their vac
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Questions and answers 337 of some s
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18 Quantum Gravity: the art of buil
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Quantum Gravity: the art of buildin
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Quantum Regge calculus 361 is given
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Quantum Regge calculus 363 group. W
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Quantum Regge calculus 365 emanatin
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Quantum Regge calculus 367 We will
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Quantum Regge calculus 369 reason,
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Quantum Regge calculus 371 gravitat
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Quantum Regge calculus 373 where ξ
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Quantum Regge calculus 375 [4] J. W
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Quantum Regge calculus 377 [52] M.
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Consistent discretizations as a roa
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21 The causal set approach to Quant
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The causal set approach to Quantum
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22 Quantum Gravity phenomenology G.
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Quantum Gravity phenomenology 429 T
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Quantum Gravity phenomenology 431 t
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Quantum Gravity phenomenology 433 c
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Quantum Gravity phenomenology 435 p
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Quantum Gravity phenomenology 437 F
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Quantum Gravity phenomenology 439 l
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Quantum Gravity phenomenology 441 p
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Quantum Gravity phenomenology 443 w
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Quantum Gravity phenomenology 445 i
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Quantum Gravity phenomenology 447 s
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Quantum Gravity phenomenology 449 [
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Quantum Gravity and precision tests
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Algebraic approach to Quantum Gravi
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25 Doubly special relativity J. KOW
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Doubly special relativity 495 DSR t
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Doubly special relativity 497 On th
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Doubly special relativity 499 some
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Doubly special relativity 501 [x 0
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Doubly special relativity 503 that
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Doubly special relativity 505 can b
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Doubly special relativity 507 scale
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26 From 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. Cr
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Questions and answers 573 frame. Ju
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Questions and answers 575 - A - J.
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Questions and answers 577 where thi
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Questions and answers 579 would all
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Index 581 cosmology, 26, 155, 184,
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Index 583 emergent, 99, 109, 163, 1
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Approaches to Quantum Gravity

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