New Paths Towards Quantum Gravity (Lecture Notes in Physics, 807)

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“We must know - we will know!”“I still need to f<strong>in</strong>d help”, said K. “Youlook for too much help from peopleyou don’t know”, said the priestdisapprov<strong>in</strong>gly. “Can you really notsee that’s not the help you need?”David Hilbert, 8th of September 1930 Franz Kafka, The Trial, undatedAddress to the Society of German Translation by David WyllieScientists and Physicians at Königsberg
Page 2 and 3: Lecture Notes in PhysicsFounding Ed
Page 4 and 5: Bernhelm Booß-BavnbekGiampiero Esp
Page 8 and 9: ForewordThis volume contains the ex
Page 10 and 11: PrefaceIn this volume we have colle
Page 12 and 13: PrefacexiGracia-Bondía devotes som
Page 14 and 15: PrefacexiiiContrary to the Ambjørn
Page 16 and 17: ContentsPart IThree Physics Visions
Page 18 and 19: Contentsxvii3.6 Finite-Dimensional
Page 20 and 21: Contentsxix6.3.2 Poisson-Delaunay S
Page 22 and 23: 4 J.M. Gracia-BondíaMy account of
Page 24 and 25: 6 J.M. Gracia-Bondíanow. The Milgr
Page 26 and 27: 8 J.M. Gracia-BondíaθAIIBILxP 1P
Page 28 and 29: 10 J.M. Gracia-Bondía1.2.1 Noncomm
Page 30 and 31: 12 J.M. Gracia-BondíaFig. 1.4 Depe
Page 32 and 33: 14 J.M. Gracia-Bondíaa simple less
Page 34 and 35: 16 J.M. Gracia-Bondía〈·, ·〉
Page 36 and 37: 18 J.M. Gracia-Bondíaδϕ =−2λ(
Page 38 and 39: 20 J.M. Gracia-BondíaƔβγ α = 1
Page 40 and 41: 22 J.M. Gracia-BondíaIn particular
Page 42 and 43: 24 J.M. Gracia-Bondías(R 2 (x, y)
Page 44 and 45: 26 J.M. Gracia-Bondías = s 0 + λs
Page 46 and 47: 28 J.M. Gracia-Bondíawith i = 1, 2
Page 48 and 49: 30 J.M. Gracia-BondíaThe two ±2 h
Page 50 and 51: 32 J.M. Gracia-Bondíaare equivalen
Page 52 and 53: 34 J.M. Gracia-Bondíaindicated by
Page 54 and 55: 36 J.M. Gracia-Bondía(1) Keep clos
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38 J.M. Gracia-BondíaIf we have re
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40 J.M. Gracia-Bondía1.5.4 On the
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42 J.M. Gracia-Bondía{T θ := a =
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44 J.M. Gracia-Bondíawhere now A i
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46 J.M. Gracia-Bondía1.5.8 Closing
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48 J.M. Gracia-Bondía1.5.8.2 What
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50 J.M. Gracia-Bondíaand dequantiz
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52 J.M. Gracia-BondíaThe first nam
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54 J.M. Gracia-Bondíabasic trouble
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56 J.M. Gracia-Bondía39. T. Kugo,
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58 J.M. Gracia-Bondía98. H. Steina
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60 J. Ambjørn et al.is now just an
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62 J. Ambjørn et al.Fig. 2.1 The f
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64 J. Ambjørn et al.such that the
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66 J. Ambjørn et al.regularization
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68 J. Ambjørn et al.the quantum me
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70 J. Ambjørn et al.ξ = N (3,2)4/
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72 J. Ambjørn et al.Fig. 2.5 The p
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74 J. Ambjørn et al.where strictly
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76 J. Ambjørn et al.spatial size o
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78 J. Ambjørn et al.In (23), √ g
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80 J. Ambjørn et al.Fig. 2.9 Analy
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82 J. Ambjørn et al.0.120 10 10 20
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84 J. Ambjørn et al.0.100.05_0.00a
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86 J. Ambjørn et al.0.060.050.04k
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88 J. Ambjørn et al.∞∑∫Z(Λ,
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90 J. Ambjørn et al.Analogously, w
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92 J. Ambjørn et al.Let w(g, z) de
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94 J. Ambjørn et al.Fig. 2.15 Root
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96 J. Ambjørn et al.= + +++. . .+F
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98 J. Ambjørn et al.( )1 2b−5w h
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100 J. Ambjørn et al.w(μ, λ 1 ,.
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102 J. Ambjørn et al.for the singu
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104 J. Ambjørn et al.In the analys
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106 J. Ambjørn et al.h 3 − h +2G
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108 J. Ambjørn et al.such a bound
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110 J. Ambjørn et al.αβ....γα
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112 J. Ambjørn et al.problem is gi
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114 J. Ambjørn et al.where the sec
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116 J. Ambjørn et al.tion as a cut
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118 J. Ambjørn et al.F ± (z) = π
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120 J. Ambjørn et al.The resulting
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122 J. Ambjørn et al.Zohren who ha
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124 J. Ambjørn et al.46. J. Ambjø
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126 N. Reshetikhinelements of the C
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128 N. Reshetikhin3.2.2 Local Lagra
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130 N. ReshetikhinThe Euler-Lagrang
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132 N. Reshetikhinwhere U is a G-in
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134 N. ReshetikhinThe Lagrangian su
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136 N. ReshetikhinSince C ∞ (N) i
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138 N. Reshetikhinσ(f ) : H(N 1 )
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140 N. Reshetikhin3.4.2.2 Statistic
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142 N. ReshetikhinAfter change of v
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144 N. Reshetikhinm......n 3 n 4Fig
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146 N. Reshetikhin.i 1i 2i n∂ n g
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148 N. Reshetikhinpermuted. But suc
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150 N. Reshetikhinthe algebra of se
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152 N. Reshetikhin3.5.4 Charged Fer
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154 N. ReshetikhinInstead of assumi
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156 N. ReshetikhinExpressing det(L(
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158 N. Reshetikhin3.6.3 Gauge Indep
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160 N. Reshetikhini j ( (a) − 1 )
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162 N. Reshetikhinwhere 〈[l], a]
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164 N. ReshetikhinLet U t (q 2 , q
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166 N. Reshetikhinexpansion asZ t (
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168 N. ReshetikhinZ M (b) =C ∑ (
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170 N. Reshetikhin∫Z M (b) =i ∗
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172 N. ReshetikhinMoreover, the ren
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174 N. ReshetikhinThe integrals (51
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176 N. ReshetikhinD 2 A = A = d
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a 1 x 1 a 2 x 2 a 3 x 3f a1 a 2 a 3
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180 N. ReshetikhinThe exponent iπ
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182 N. ReshetikhinFinally, all thes
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184 N. Reshetikhinedge is incoming,
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186 N. ReshetikhinHere the coeffici
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188 N. Reshetikhin(Z M RT ∼ 1|Z(G
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190 N. Reshetikhin34. C. Itsykson,
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194 I.G. AvramidiIn this situation
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196 I.G. AvramidiLet us consider a
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198 I.G. AvramidiδS = 〈J,ϕ〉.
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200 I.G. AvramidiFurthermore, the s
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202 I.G. AvramidiNow, by expanding
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204 I.G. Avramidisubspace M 0 , whi
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206 I.G. AvramidiThe parameters of
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208 I.G. AvramidiIn this gauge the
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210 I.G. Avramidithe generators of
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212 I.G. AvramidiThus, a Laplace-ty
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214 I.G. AvramidiU(t|x, x ′ ) =
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216 I.G. AvramidiNote that y a = 0a
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218 I.G. AvramidiMoreover, the valu
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220 I.G. Avramidi4.3.4.2 Asymptotic
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222 I.G. Avramidistructure of diago
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224 I.G. Avramidi[(n+1)/2]−2∑G
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226 I.G. Avramidicomputed from (122
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228 I.G. Avramidia k =(1 + 1 ) −1
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230 I.G. Avramidi4.5.3 Matrix Algor
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232 I.G. AvramidiFrom dimensional a
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234 I.G. Avramidia diag1= Q − 1 6
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236 I.G. Avramidi4.6 High-Energy Ap
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238 I.G. Avramidif (1) (ξ) = 1 , (
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240 I.G. Avramidiof covariant deriv
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242 I.G. AvramidiExpanding it in a
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244 I.G. Avramidi∮C(t) =∮K (t)
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246 I.G. Avramidipoint x ′ by mul
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248 I.G. AvramidiFor the lack of a
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250 I.G. AvramidiG YM realizing a r
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252 I.G. AvramidiThen one can show
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254 I.G. Avramidibelow are well def
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256 I.G. Avramidiwhere ζ ˆL (s) a
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258 I.G. Avramidi(V(1)) ab = 2R a b
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Chapter 5Lectures on Cohomology, T-
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5 Lectures on Cohomology, T-Duality
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314 H. Zessin6.1 An Axiomatic Intro
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316 H. Zessinand ask for its asympt
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318 H. Zessin((x,η)∈ D, a ∈ R
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320 H. Zessin6.2.4 The Cluster Proc
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322 H. ZessinDenote this subset of
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324 H. Zessincircumball of x, i.e.
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326 H. ZessinNow (x,η) is an admis
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328 H. ZessinThus Q realizes config
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330 H. ZessinLemma 5 (ϕ ) ∈K is
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332 H. ZessinWithin this example co
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334 H. Zessin6.6 Comments and Final
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Chapter 7Steps Towards Quantum Grav
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7 Steps Towards Quantum Gravity and
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IndexAAbstract constructions, 346Ac
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Index 357HHabits, 352Hadamard - Min
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Index 359Theory, 339-342, 344, 346,
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New Paths Towards Quantum Gravity (Lecture Notes in Physics, 807)

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