Quantum Field Theory and Gravity: Conceptual and Mathematical ...

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Discrete and Continuum Third Quantization of Gravity 63 [21] P. Ginsparg. Matrix models of 2d gravity. 1991. [22] Florian Girelli, Etera R. Livine, and Daniele Oriti. 4d deformed special relativity from group field theories. Phys. Rev. D, 81:024015, 2010. [23] Domenico Giulini. The superspace of geometrodynamics. General Relativity and Gravitation, 41:785–815, April 2009. [24] Razvan Gurau. The 1/N expansion of colored tensor models. 2010. [25] Razvan Gurau and Vincent Rivasseau. The 1/N expansion of colored tensor models in arbitrary dimension. 2011. [26] Jonathan J. Halliwell and Miguel E. Ortiz. Sum-over-histories origin of the composition laws of relativistic quantum mechanics and quantum cosmology. Physical Review D, 48:748–768, July 1993. [27] G. T. Horowitz. Topology change in classical and quantum gravity. Classical and Quantum Gravity, 8:587–601, April 1991. [28] B. L. Hu. Can spacetime be a condensate? Int. J. Theor. Phys., 44:1785–1806, 2005. [29] Karel Kuchař. General relativity: dynamics without symmetry. Journal of Mathematical Physics, 22:2640–2654, November 1981. [30] E. Livine, D. Oriti, and J. Ryan. Effective Hamiltonian constraint from group field theory, in preparation. [31] Etera R. Livine. Projected spin networks for Lorentz connection: linking spin foams and loop gravity. Classical and Quantum Gravity, 19:5525–5541, November 2002. [32] Jacques Magnen, Karim Noui, Vincent Rivasseau, and Matteo Smerlak. Scaling behaviour of three-dimensional group field theory. Class. Quant. Grav., 26:185012, 2009. [33] Karim Noui and Alejandro Perez. Three-dimensional loop quantum gravity: physical scalar product and spin-foam models. Classical and Quantum Gravity, 22:1739–1761, May 2005. [34] D. Oriti. The microscopic dynamics of quantum space as a group field theory, in: Foundations of space and time, G. Ellis, J. Murugan (eds.). Cambridge: Cambridge University Press, 2011. [35] Daniele Oriti. Spacetime geometry from algebra: spin foam models for nonperturbative quantum gravity. Reports on Progress in Physics, 64:1489–1543, December 2001. [36] Daniele Oriti. Spin foam models of quantum spacetime. PhD thesis, University of Cambridge, 2003. [37] Daniele Oriti. Quantum gravity as a quantum field theory of simplicial geometry, in: Mathematical and Physical Aspects of Quantum Gravity, B. Fauser, J. Tolksdorf and E. Zeidler (eds.). Birkhäuser, Basel, 2006. [38] Daniele Oriti. The group field theory approach to quantum gravity. 2006. [39] Daniele Oriti. Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity. 2007. [40] Daniele Oriti. Approaches to quantum gravity: toward a new understanding of space, time and matter. Cambridge: Cambridge Univ. Press, 2009. [41] Daniele Oriti and Lorenzo Sindoni. Towards classical geometrodynamics from group field theory hydrodynamics. New J. Phys., 13:025006, 2011.
64 S. Gielen and D. Oriti [42] Alejandro Perez. Spin foam models for quantum gravity. Classical and Quantum Gravity, 20(6):R43, 2003. [43] G. Ponzano and T. Regge. Semiclassical limit of Racah coefficients, in: Spectroscopic and Group Theoretical Methods in Physics, F. Block (ed.), 1–58. New York: John Wiley and Sons, Inc., 1968. [44] Carlo Rovelli. Quantum gravity. Cambridge University Press, 2004. [45] Carlo Rovelli. A new look at loop quantum gravity. April 2010. [46] Claudio Teitelboim. Quantum mechanics on the gravitational field. Phys. Rev. D, 25:3159–3179, June 1982. [47] Thomas Thiemann. Modern canonical quantum general relativity. Cambridge University Press, 2007. [48] Grigory Volovik. From quantum hydrodynamics to quantum gravity. 2006. [49] J. A. Wheeler. Superspace and the nature of quantum geometrodynamics, in: Quantum cosmology, L. Z. Fang, R. Ruffini (eds.), 27–92. Singapore: World Scientific, 1987. Steffen Gielen and Daniele Oriti Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 D-14476 Golm Germany e-mail: gielen@aei.mpg.de doriti@aei.mpg.de
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Quantum Field Theory and Gravity Co
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Contents Preface ..................
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Preface The present volume arose fr
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Preface ix 6. (How) can we test qua
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Preface xi Felix Finster, Andreas G
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Preface xiii it is related to other
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Quantum Gravity: Whence, Whither? C
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Quantum Gravity: Whence, Whither? 3
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Page 28: Quantum Gravity: Whence, Whither? 1
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Page 37 and 38: 22 K. Fredenhagen and K. Rejzner 5.
Page 40 and 41: The “Big Wave” Theory for Dark
Page 56 and 57: Discrete and Continuum Third Quanti
Page 80 and 81: Unsharp Values, Domains and Topoi A
Page 82 and 83: Unsharp Values, Domains and Topoi 6
Page 112 and 113: Causal Boundary of Spacetimes: Revi
Page 114 and 115: Causal Boundaries 99 to the Gromov
Page 116 and 117: Causal Boundaries 101 I + (ρ) ρ P
Page 118 and 119: Causal Boundaries 103 Figure 2. The
Page 120 and 121: Causal Boundaries 105 more pairings
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Causal Boundaries 113 respectively.
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Causal Boundaries 115 6.3. Structur
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Causal Boundaries 117 Qualitative F
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Causal Boundaries 119 [26] E. Mingu
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122 D. Häfner Let us give an idea
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124 D. Häfner Figure 1. The collap
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126 D. Häfner Figure 2. The manifo
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128 D. Häfner and the angular mome
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130 D. Häfner Lemma 3.5. There exi
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132 D. Häfner Proposition 4.4. The
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134 D. Häfner 6. Strategy of the p
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136 D. Häfner [3] B. Carter, Black
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138 R. Oeckl it is less compelling
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140 R. Oeckl Depending on the theor
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142 R. Oeckl 2.3. Recovery of stand
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144 R. Oeckl where the condition A
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146 R. Oeckl Before we proceed to i
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148 R. Oeckl the complex classical
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150 R. Oeckl The corresponding anni
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152 R. Oeckl Proposition 4.1 (Coher
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154 R. Oeckl much larger than the s
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156 R. Oeckl Setting F equal to F
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158 F. Finster, A. Grotz and D. Sch
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184 C. Bär and N. Ginoux treat the
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186 C. Bär and N. Ginoux the categ
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188 C. Bär and N. Ginoux Example 2
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190 C. Bär and N. Ginoux 3.2. Diff
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192 C. Bär and N. Ginoux In other
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194 C. Bär and N. Ginoux Here (e j
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196 C. Bär and N. Ginoux Remark 3.
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198 C. Bär and N. Ginoux Proof. Th
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200 C. Bär and N. Ginoux To prove
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202 C. Bär and N. Ginoux We refer
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204 C. Bär and N. Ginoux where Glo
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206 C. Bär and N. Ginoux [24] R. M
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208 C. J. Fewster well-described by
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210 C. J. Fewster and J + M (p) ∩
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212 C. J. Fewster commute. As funct
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214 C. J. Fewster ι + ι − M +
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216 C. J. Fewster ϕ(ψ) M M ϕ(M)(
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218 C. J. Fewster theory. The resul
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220 C. J. Fewster Following [7], a
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222 C. J. Fewster Sketch of proof.
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224 C. J. Fewster The relative Cauc
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226 C. J. Fewster [2] Bär, C., Gin
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Local Covariance, Renormalization A
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Local Thermal Equilibrium and Cosmo
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Shape Dynamics. An Introduction Jul
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Shape Dynamics. An Introduction 259
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where dx bm a Shape Dynamics. An In
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300 M. Kiessling In the following,
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302 M. Kiessling where “δ( · )
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304 M. Kiessling the point charge,
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306 M. Kiessling (2.17) and (2.18)
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308 M. Kiessling Maxwell’s “law
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310 M. Kiessling argued that E f (
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312 M. Kiessling the Maxwell-Born-I
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314 M. Kiessling removal. For insta
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316 M. Kiessling ∂ 4πc that for
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318 M. Kiessling d dt Dirac, on the
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320 M. Kiessling The Lorenz-Lorentz
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322 M. Kiessling ( 1 c Lorentz and
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324 M. Kiessling potential fields
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326 M. Kiessling as I have done her
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328 M. Kiessling just the Hamilton-
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330 M. Kiessling 7. Closing remarks
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332 M. Kiessling [Bor1937] Born, M.
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334 M. Kiessling [Lié1898] Liénar
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How Unique Are Higher-dimensional B
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Equivalence Principle, Quantum Mech
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Atom Interferometry 347 The second
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Atom Interferometry 349 α CR , aim
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Atom Interferometry 351 of this mas
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Atom Interferometry 353 height B A
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Atom Interferometry 355 iff ψ = (
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Atom Interferometry 357 have be rea
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Atom Interferometry 359 where F (t
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Atom Interferometry 361 5.2. Interf
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Atom Interferometry 363 Evaluating
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Atom Interferometry 365 where the l
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Atom Interferometry 367 Then they s
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Atom Interferometry 369 [8] T.M. Fo
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Index n-point function, 51, 146, 23
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Index 373 conformal field theory, 1
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Index 375 gravitational redshift, 2
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Index 377 operator product, 138 par
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Index 379 standard model of particl
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