Book contents
- Frontmatter
- Contents
- List of contributors
- 1 The problem with quantum gravity
- 2 A dialogue on the nature of gravity
- 3 Effective theories and modifications of gravity
- 4 The small-scale structure of spacetime
- 5 Ultraviolet divergences in supersymmetric theories
- 6 Cosmological quantum billiards
- 7 Progress in RNS string theory and pure spinors
- 8 Recent trends in superstring phenomenology
- 9 Emergent spacetime
- 10 Loop quantum gravity
- 11 Loop quantum gravity and cosmology
- 12 The microscopic dynamics of quantum space as a group field theory
- 13 Causal dynamical triangulations and the quest for quantum gravity
- 14 Proper time is stochastic time in 2D quantum gravity
- 15 Logic is to the quantum as geometry is to gravity
- 16 Causal sets: discreteness without symmetry breaking
- 17 The Big Bang, quantum gravity and black-hole information loss
- 18 Conversations in string theory
- Index
- References
13 - Causal dynamical triangulations and the quest for quantum gravity
Published online by Cambridge University Press: 05 August 2012
Book contents
- Frontmatter
- Contents
- List of contributors
- 1 The problem with quantum gravity
- 2 A dialogue on the nature of gravity
- 3 Effective theories and modifications of gravity
- 4 The small-scale structure of spacetime
- 5 Ultraviolet divergences in supersymmetric theories
- 6 Cosmological quantum billiards
- 7 Progress in RNS string theory and pure spinors
- 8 Recent trends in superstring phenomenology
- 9 Emergent spacetime
- 10 Loop quantum gravity
- 11 Loop quantum gravity and cosmology
- 12 The microscopic dynamics of quantum space as a group field theory
- 13 Causal dynamical triangulations and the quest for quantum gravity
- 14 Proper time is stochastic time in 2D quantum gravity
- 15 Logic is to the quantum as geometry is to gravity
- 16 Causal sets: discreteness without symmetry breaking
- 17 The Big Bang, quantum gravity and black-hole information loss
- 18 Conversations in string theory
- Index
- References
Summary
Quantum gravity by causal dynamical triangulation has over the last few years emerged as a serious contender for a nonperturbative description of the theory. It is a nonperturbative implementation of the sum-overhistories, which relies on few ingredients and initial assumptions, has few free parameters and – crucially – is amenable to numerical simulations. It is the only approach to have demonstrated that a classical universe can be generated dynamically from Planckian quantum fluctuations. At the same time, it allows for the explicit evaluation of expectation values of invariants characterizing the highly nonclassical, short-distance behaviour of spacetime. As an added bonus, we have learned important lessons on which aspects of spacetime need to be fixed a priori as part of the background structure and which can be expected to emerge dynamically.
Quantum gravity – taking a conservative stance
Many fundamental questions about the nature of space, time and gravitational interactions are not answered by the classical theory of general relativity, but lie in the realm of the still-searched-for theory of quantum gravity: What is the quantum theory underlying general relativity, and what does it say about the quantum origins of space, time and our universe? What is the microstructure of spacetime at the shortest scale usually considered, the Planck scale lPl = 10-35m, and what are the relevant degrees of freedom determining the dynamics there?
- Type
- Chapter
- Information
- Foundations of Space and TimeReflections on Quantum Gravity, pp. 321 - 337Publisher: Cambridge University PressPrint publication year: 2012
References
[1] and : Non-perturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys.B 536 (1998) 407–34 [hep-th/9805108].Google Scholar
[2] and : Properties of loop equations for the Hermitean matrix model and for two-dimensional quantum gravity, Mod. Phys. Lett.A 5 (1990) 1753–64;Google Scholar
, and : Multiloop correlators for two-dimensional quantum gravity, Phys. Lett.B 251 (1990) 517–24.Google Scholar
[3] , and : A new perspective on matter coupling in 2d quantum gravity, Phys. Rev.D 60 (1999) 104035 [hep-th/9904012];Google Scholar
Crossing the c = 1 barrier in 2d Lorentzian quantum gravity, Phys. Rev.D 61 (2000) 044010 [hep-lat/9909129].
[4] , and : A nonperturbative Lorentzian path integral for gravity, Phys. Rev. Lett. 85 (2000) 924–7 [hep-th/0002050];Google Scholar
Dynamically triangulating Lorentzian quantum gravity, Nucl. Phys.B 610 (2001) 347–82 [hep-th/0105267].
[5] , and : Lorentzian and Euclidean quantum gravity: Analytical and numerical results, in: Proceedings of M-Theory and Quantum Geometry, 1999 NATO Advanced Study Institute, Akureyri Island, eds. et al. (Kluwer, 2000) 382–449 [hep-th/0001124].
[6] , and : Nonperturbative 3-d Lorentzian quantum gravity, Phys. Rev.D 64 (2001) 044011 [hep-th/0011276].Google Scholar
[7] , and : Emergence of a 4D world from causal quantum gravity, Phys. Rev. Lett. 93 (2004) 131301 [hep-th/0404156].Google Scholar
[8] , and : Spectral dimension of the universe, Phys. Rev. Lett. 95 (2005) 171301 [hep-th/0505113].Google Scholar
[9] , and : Reconstructing the universe, Phys. Rev.D 72 (2005) 064014 [hep-th/0505154].Google Scholar
[10] , , and : Planckian birth of the quantum de Sitter universe, Phys. Rev. Lett. 100 (2008) 091304 [arXiv:0712.2485, hep-th].Google Scholar
[11] , , , and : A string field theory based on Causal Dynamical Triangulations, JHEP 0805 (2008) 032 [arXiv:0802.0719, hep-th].Google Scholar
[12] , , and : Shaken, but not stirred – Potts model coupled to quantum gravity, Nucl. Phys.B 807 (2009) 251 [arXiv:0806.3506, hep-lat].Google Scholar
[13] , , and : The nonperturbative quantum de Sitter universe, Phys. Rev.D 78 (2008) 063544 [arXiv:0807.4481, hep-th].Google Scholar
The self-organized de Sitter universe, Int. J. Mod. Phys.D 17 (2009) 2515–20 [arXiv:0806.0397, gr-qc].
[15] , and : Quantum gravity as sum over spacetimes [arXiv:0906.3947, gr-qc];
Quantum gravity, or the art of building spacetime, in: Approaches to Quantum Gravity, ed. , Cambridge University Press (2009) 341–59 [hep-th/0604212];
: The emergence of spacetime, or, Quantum gravity on your desktop, Class. Quant. Grav. 25 (2008) 114006 [arXiv:0711.0273, gr-qc];Google Scholar
[16] , , and ; Summing over all topologies in CDT string field theory, Phys. Lett.B 678 (2009) 227 [arXiv:0905.2108, hep-th].Google Scholar
[17] , , , and : Proper time is stochastic time in 2d quantum gravity [arXiv:0911.4211, hep-th].
[18] : Further evidence that the transition of 4D dynamical triangulation is 1st order, Phys. Lett.B 389 (1996) 238 [hep-lat/9603024].Google Scholar
[19] and : Diffusion and Reactions in Fractals and Disordered Systems, Cambridge University Press (2000).
[20] and : Spectral geometry as a probe of quantum spacetime, Phys. Rev.D 80 (2009) 124036 [arXiv:0911.0401, hep-th].Google Scholar
[21] , , and : Focusing on the fixed point of 4d simplicial gravity, Nucl. Phys.B 472 (1996) 293 [hep-lat/9601024].Google Scholar
[22] , , and : Appearance of mother universe and singular vertices in random geometries, Nucl. Phys.B 495 (1997) 463 [hep-lat/9608030].Google Scholar
[23] : Issues in the philosophy of cosmology [astro-ph/0602280].
[24] and (eds): Euclidean Quantum Gravity, World Scientific, Singapore (1993).
[25] : Nonlocality vs. complementarity: a conservative approach to the information problem [arXiv:0911.3395, hep-th].
[26] and : Steepest descent contours in the path integral approach to quantum cosmology. 3. A general method with applications to anisotropic minisuperspace models, Phys. Rev.D 42 (1990) 3997–4031.Google Scholar
[27] : The causal set approach to quantum gravity, in: Approaches to Quantum Gravity, ed. , Cambridge University Press (2009) 393–413 [gr-qc/0601121].
[28] : Emergent quantum mechanics and emergent symmetries, AIP Conf. Proc. 957 (2007) 154 [arXiv:0707.4568, hep-th].Google Scholar
[29] : Spectral dimension of the universe in quantum gravity at a Lifshitz point, Phys. Rev. Lett. 102 (2009) 161301 [arXiv:0902.3657, hep-th].Google Scholar
[30] , and : Coupling point-like masses to quantum gravity with causal dynamical triangulations, preprint Utrecht U., Class Quant. Grav. 27 (2010) 185025 [arXiv:1002.4618, gr-qc].Google Scholar
[31] : Quantum Gravity, 2nd edn, Oxford University Press (2007).
[32] and : Ultraviolet fixed point and generalized flow equation of quantum gravity, Phys. Rev.D 65 (2002) 025013 [hep-th/0108040].Google Scholar
[33] and : Fractal spacetime structure in asymptotically safe gravity, JHEP 0510 (2005) 050 [hep-th/0508202].Google Scholar
[34] : The volume operator in discretized quantum gravity, Phys. Rev. Lett. 75 (1995) 3048 [gr-qc/9506014].Google Scholar
[35] and : Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity, Class. Quant. Grav. 23 (2006) 465 [hep-th/0306183].Google Scholar
[36] , and : Taming the cosmological constant in 2D causal quantum gravity with topology change, Nucl. Phys.B 751 (2006) 419 [hep-th/0507012].Google Scholar
[37] : Can causal dynamical triangulations probe factor-ordering issues?, Acta Phys. Polon. B Proc. Suppl. 2 (2009) 563 [arXiv:0910.2117, gr-qc].Google Scholar
[38] and : Monte Carlo Methods in Statistical Physics, Clarendon Press, Oxford (1999).
[39] : The asymptotic safety scenario in quantum gravity: An introduction, Class. Quant. Grav. 24 (2007) R171 [gr-qc/0610018].Google Scholar
[40] and : The asymptotic safety scenario in quantum gravity, Living Rev. Rel. 9 (2006) 5.Google Scholar
[41] and : Methods of Modern Mathematical Physics, vol. 2, Academic Press (1975).
[43] and : Discreteness of area and volume in quantum gravity, Nucl. Phys.B 442 (1995) 593;Google Scholar
Erratum-Discreteness of area and volume in quantum gravity, Nucl. Phys.B 456 (1995) 753 [gr-qc/9411005].
[44] : Loop quantum gravity: An inside view, Lect. Notes Phys. 721 (2007) 185 [hep-th/0608210].Google Scholar
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