Approaches to Quantum Gravity

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The group field theory approach to Quantum Gravity 331 [33] E. Livine, D. Oriti, JHEP 0702, 092 (2007), gr-qc/0512002. [34] D. Oriti, J. Ryan, Class. Quant. Grav. 23 (2006) 6543, gr-qc/0602010. [35] L. Freidel, D. Oriti, J. Ryan (2005), gr-qc/0506067. [36] W. Fairbairn, E. Livine (2007), gr-qc/0702125. [37] L. Crane (2001), gr-qc/0110060. [38] S. Alexandrov, E. Livine, Phys. Rev. D 67 (2003) 044009, gr-qc/0209105. [39] F. Markopoulou, L. Smolin, Nucl. Phys. B 508 (1997) 409, gr-qc/9702025. [40] R. Oeckl, Nucl. Phys. B 657 (2003) 107, gr-qc/0212047. [41] F. Markopoulou, Class. Quant. Grav. 20 (2003) 777, gr-qc/0203036. [42] G. Volovik, Phys. Rept. 351 (2001) 195, gr-qc/0005091. [43] C. Barcelo, S. Liberati, M. Visser, Living Rev. Rel. 8 (2005) 12, gr-qc/0505065. [44] D. Oriti (2006), hep-th/0612301.
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APPROACHES TO QUANTUM GRAVITY Towar
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A Sandra
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viii Contents 11 String theory, hol
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Contributors J. Ambjørn The Niels
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xii List of contributors D. Oriti M
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Preface Quantum Gravity is a dream,
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Preface xvii are following in their
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Preface xix enormous amount of prog
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1 Unfinished revolution C. ROVELLI
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Unfinished revolution 5 wit of empi
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Unfinished revolution 7 In general
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Unfinished revolution 9 However, re
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Unfinished revolution 11 References
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2 The fundamental nature of space a
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The fundamental nature of space and
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Does locality fail at intermediate
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∫ Does locality fail at intermedi
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Prolegomena to any future Quantum G
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Spacetime symmetries in histories c
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Categorical geometry and the mathem
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7 Emergent relativity O. DREYER 7.1
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A (a) Emergent relativity 101 (b) (
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Emergent relativity 103 It is here
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Emergent relativity 105 spacetime c
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Emergent relativity 107 φ A B Fig.
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Emergent relativity 109 If, on the
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8 Asymptotic safety R. PERCACCI 8.1
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Asymptotic safety 113 field and the
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Asymptotic safety 115 For example,
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Asymptotic safety 117 If we choose
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Asymptotic safety 119 complex field
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Asymptotic safety 121 2 G ~ ~ 1.5 1
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Asymptotic safety 123 larger, and i
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Asymptotic safety 125 Dimensional a
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Asymptotic safety 127 References [1
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9 New directions in background inde
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New directions in background indepe
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Questions and answers 151 Quantum G
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Questions and answers 153 was that
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Questions and answers 155 causality
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Questions and answers 157 to hold),
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Questions and answers 159 of how gr
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Questions and answers 161 the actio
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Questions and answers 163 allow us
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Questions and answers 165 - A-F.Mar
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10 Gauge/gravity duality G. HOROWIT
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Gauge/gravity duality 171 strong an
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Gauge/gravity duality 173 decompose
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Gauge/gravity duality 175 Here l s
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Gauge/gravity duality 177 There is
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Gauge/gravity duality 179 these are
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Gauge/gravity duality 181 leading t
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Gauge/gravity duality 183 states to
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Gauge/gravity duality 185 [6] N. Be
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11 String theory, holography and Qu
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String theory, holography and Quant
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String field theory 211 no tools to
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String field theory 213 made an ins
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(d) Cyclicity: ∫ ⋆= (−1) G G
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String field theory 217 however, th
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String field theory 219 12.2.3 Outs
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String field theory 221 a review) g
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String field theory 223 similar com
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String field theory 225 this; the p
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String field theory 227 [11] T. G.
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Questions and answers • Q - D. Or
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Questions and answers 231 condition
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Part III Loop quantum gravity and s
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236 T. Thiemann (anti)commute. We s
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238 T. Thiemann Notice that in gene
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240 T. Thiemann spectrum of all the
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242 T. Thiemann order to avoid anom
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244 T. Thiemann We consider spaceti
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246 T. Thiemann Hence both gauge gr
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248 T. Thiemann that Ĉ(N) cannot b
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250 T. Thiemann [8] R. Brunetti, K.
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252 T. Thiemann [48] M. Bojowald, H
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254 E. Livine SU(2) gauge theory. T
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256 E. Livine space; η IJ is the f
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258 E. Livine However, in contrast
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260 E. Livine (i) Either we work wi
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262 E. Livine At the end of the day
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264 E. Livine projector at the end
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266 E. Livine for a surface S inter
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268 E. Livine This constraint is sa
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270 E. Livine we do not need the se
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15 The spin foam representation of
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274 A. Perez in classical general r
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276 A. Perez where M = ×R (for an
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278 A. Perez the Levi-Civita tensor
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280 A. Perez k Tr[ k (W p )] ✄ j
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282 A. Perez j j j k j k m k m j j
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284 A. Perez Here we studied the in
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286 A. Perez A spin foam representa
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288 A. Perez master-constraint prog
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16 Three-dimensional spin foam Quan
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292 L. Freidel 16.3 The Ponzano-Reg
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294 L. Freidel under usual gauge tr
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296 L. Freidel is now constrained t
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298 L. Freidel 16.4.1 Mathematical
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300 L. Freidel Therefore, at first
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302 L. Freidel The inverse group Fo
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304 L. Freidel From this identity,
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Page 662: 17 The group field theory approach
Page 666: 312 D. Oriti simplicial complex, or
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Page 686: 322 D. Oriti or SO(3, 1)) [8; 9; 10
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Page 698: 328 D. Oriti research. On the other
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Page 708: Questions and answers 333 the holes
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Quantum Gravity: the art of buildin
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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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