Approaches to Quantum Gravity

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Part IVDiscrete <strong>Quantum</strong> <strong>Gravity</strong>
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APPROACHES TO QUANTUM GRAVITYToward
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A Sandra
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viiiContents11 String theory, holog
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ContributorsJ. AmbjørnThe Niels Bo
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xiiList of contributorsD. OritiMax
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PrefaceQuantum Gravity is a dream,
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Prefacexviiare following in their s
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Prefacexixenormous amount of progre
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1Unfinished revolutionC. ROVELLIOne
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Unfinished revolution 5wit of empir
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Unfinished revolution 7In general r
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Unfinished revolution 9However, res
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Unfinished revolution 11References[
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2The fundamental nature of space an
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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 intermedia
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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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7Emergent relativityO. DREYER7.1 In
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A(a)Emergent relativity 101(b)(c)B(
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Emergent relativity 103It is here t
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Emergent relativity 105spacetime co
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Emergent relativity 107φABFig. 7.4
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Emergent relativity 109If, on the o
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8Asymptotic safetyR. PERCACCI8.1 In
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Asymptotic safety 113field and the
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Asymptotic safety 115For example, t
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Asymptotic safety 117If we choose k
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Asymptotic safety 119complex fields
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Asymptotic safety 1212G ~ ~1.510.5-
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Asymptotic safety 123larger, and it
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Asymptotic safety 125Dimensional an
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Asymptotic safety 127References[1]
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9New directions in background indep
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New directions in background indepe
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Questions and answers 151Quantum Gr
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Questions and answers 153was that t
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Questions and answers 155causality
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Questions and answers 157to hold),
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Questions and answers 159of how gra
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Questions and answers 161the action
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Questions and answers 163allow us t
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Questions and answers 165- A-F.Mark
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10Gauge/gravity dualityG. HOROWITZ
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Gauge/gravity duality 171strong and
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Gauge/gravity duality 173decomposed
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Gauge/gravity duality 175Here l s i
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Gauge/gravity duality 177There is a
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Gauge/gravity duality 179these are
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Gauge/gravity duality 181leading to
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Gauge/gravity duality 183states to
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Gauge/gravity duality 185[6] N. Ber
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11String theory, holography and Qua
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String theory, holography and Quant
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String field theory 211no tools to
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String field theory 213made an insi
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(d) Cyclicity: ∫ ⋆= (−1) G G
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String field theory 217however, the
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String field theory 21912.2.3 Outst
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String field theory 221a review) gi
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String field theory 223similar comp
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String field theory 225this; the ph
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String field theory 227[11] T. G. E
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Questions and answers• Q - D. Ori
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Questions and answers 231condition
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Part IIILoop quantum gravity and sp
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236 T. Thiemann(anti)commute. We se
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238 T. ThiemannNotice that in gener
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240 T. Thiemannspectrum of all the
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242 T. Thiemannorder to avoid anoma
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244 T. ThiemannWe consider spacetim
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246 T. ThiemannHence both gauge gro
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248 T. Thiemannthat Ĉ(N) cannot be
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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. LivineSU(2) gauge theory. Th
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256 E. Livinespace; η IJ is the fl
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258 E. LivineHowever, in contrast t
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260 E. Livine(i) Either we work wit
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262 E. LivineAt the end of the day,
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264 E. Livineprojector at the end v
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266 E. Livinefor a surface S inters
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268 E. LivineThis constraint is sat
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270 E. Livinewe do not need the sec
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15The spin foam representation of l
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274 A. Perezin classical general re
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276 A. Perezwhere M = ×R (for an
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278 A. Perezthe Levi-Civita tensor.
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280 A. PerezkTr[ k (W p )] ✄jP=
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282 A. Perezjjjkjkmkmjjjjmkmkmkmkkj
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284 A. PerezHere we studied the int
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286 A. PerezA spin foam representat
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288 A. Perezmaster-constraint progr
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16Three-dimensional spin foam Quant
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292 L. Freidel16.3 The Ponzano-Regg
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294 L. Freidelunder usual gauge tra
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296 L. Freidelis now constrained to
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298 L. Freidel16.4.1 Mathematical s
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300 L. FreidelTherefore, at first o
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302 L. FreidelThe inverse group Fou
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304 L. FreidelFrom this identity, i
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306 L. Freidelchoice of statistics.
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308 L. FreidelA deeper study of the
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17The group field theory approach t
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Page 724: 18Quantum Gravity: the art of build
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Page 764: 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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