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54
Quantum gravity in 2 + 1 dimensions . . .
 LIVING REVIEWS IN RELATIVITY
, 2005
"... In three spacetime dimensions, general relativity drastically simplifies, becoming a “topological” theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body o ..."
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Cited by 137 (0 self)
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In three spacetime dimensions, general relativity drastically simplifies, becoming a “topological” theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)dimensional vacuum gravity in the setting of a spatially closed universe.
Loop quantum cosmology
, 2006
"... Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical spacetime inevitably comes to an end after a ..."
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Cited by 48 (11 self)
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Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Scaling in quantum gravity
 Nucl. Phys. B
, 1995
"... The 2point function is the natural object in quantum gravity for extracting critical behavior: The exponential fall off of the 2point function with geodesic distance determines the fractal dimension dH of spacetime. The integral of the 2point function determines the entropy exponent γ, i.e. the ..."
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Cited by 42 (10 self)
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The 2point function is the natural object in quantum gravity for extracting critical behavior: The exponential fall off of the 2point function with geodesic distance determines the fractal dimension dH of spacetime. The integral of the 2point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2point function connects γ and dH by a quantum gravity version of Fisher’s scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation. 1 1
Nonperturbative 3d Lorentzian Quantum Gravity
, 2001
"... We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized nonperturbative state sum over simplicial Lorentzian spacetimes, each possessing a unique Wick rotation to Euclidean signature. We investigate here the phase structure of the Wickrotated path integra ..."
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Cited by 39 (20 self)
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We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized nonperturbative state sum over simplicial Lorentzian spacetimes, each possessing a unique Wick rotation to Euclidean signature. We investigate here the phase structure of the Wickrotated path integral in three dimensions with the aid of computer simulations. After finetuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant k0 for which the functional integral is dominated by nondegenerate threedimensional spacetimes. We therefore have a situation in which a welldefined ground state of extended geometry is generated dynamically from a nonperturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semiclassical spherical universe. Measurements so far indicate that k0 defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete Lorentzian gravity is a promising candidate for a nontrivial theory of quantum gravity.
Spin foam models of Riemannian quantum gravity
, 2002
"... Using numerical calculations, we compare three versions of the Barrett– Crane model of 4dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for many tria ..."
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Cited by 27 (4 self)
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Using numerical calculations, we compare three versions of the Barrett– Crane model of 4dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for many triangulated 4manifolds. In the version with modified face and edge amplitudes due to Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spinzero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model.
The Universe from Scratch
, 2005
"... A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19thcentury founders of modern geometry contemplated the possibility that a piece of empty space that looks completely smooth and structureless to the n ..."
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Cited by 25 (3 self)
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A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19thcentury founders of modern geometry contemplated the possibility that a piece of empty space that looks completely smooth and structureless to the naked eye might have an intricate microstructure at a much smaller scale. Our vastly increased understanding of the physical world acquired during the 20th century has made this a certainty. The laws of quantum theory tell us that looking at spacetime at ever smaller scales requires ever larger energies, and, according to Einstein’s theory of general relativity, this will alter spacetime itself: it will acquire structure in the form of curvature. What we still lack is a definitive theory of quantum gravity to give us a detailed and quantitative description of the highly curved and quantumfluctuating geometry of spacetime at this socalled Planck scale. – This article outlines a particular approach to constructing such a theory, that of Causal Dynamical Triangulations, and its achievements so far in deriving from
Coarse graining methods for spin net and spin foam models
 HOLONOMY SPIN FOAM MODELS: DEFINITION AND COARSE GRAINING,” PHYS. REV. D 87, 044048 (2013) [ARXIV:1208.3388 [GRQC
, 2011
"... We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply MigdalKadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on fini ..."
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Cited by 19 (11 self)
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We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply MigdalKadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on finite Abelian groups and introduce ‘cutoff models’ to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the Tensor Network Renormalization analysis, a new Gauß constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We