Loop-and-allied QG bibliography

[John86]

http://arxiv.org/abs/1011.0061
The Conformal Constraint in Canonical Quantum Gravity
Authors: Gerard 't Hooft
(Submitted on 30 Oct 2010)
Abstract: Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the metric fields. This should generate a conformally invariant theory as an intermediate result, where the conformal anomalies must be constrained to cancel out. When the residual metric is treated as a background, and if this background is taken to be flat, this leads to a novel constraint: in combination with the dilaton contributions, the matter lagrangian should have a vanishing beta function. The zeros of this beta function are isolated points in the landscape of quantum field theories, and so we arrive at a denumerable, or perhaps even finite, set of quantum theories for matter, where not only the coupling constants, but also the masses and the cosmological constant are all fixed, and computable, in terms of the Planck units.

http://arxiv.org/abs/1009.0669
Probing the small distance structure of canonical quantum gravity using the conformal group
Authors: Gerard 't Hooft
(Submitted on 3 Sep 2010 (v1), last revised 2 Oct 2010 (this version, v2))
Abstract: In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and the effects of a renormalization counter term are considered. It generates problems such as unitarity violation, due to a Landau-like ghost, and conformal anomalies. Adding (massive or massless) matter fields does not change the picture. Various alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles interacting with a gravitational field, in particular gravitons, which are "partly classical". This approach was inspired by a search towards the reconciliation of Hawking radiation with unitarity and locality, and it offers basic new insights there.

 

[marcus]

John the two items in your post were listed here earlier.

http://arxiv.org/abs/1009.0669
Probing the small distance structure of canonical quantum gravity using the conformal group
Gerard 't Hooft
...

http://arxiv.org/abs/1011.0061
The Conformal Constraint in Canonical Quantum Gravity
Authors: Gerard 't Hooft
...

If you would like to delete your post, I will delete this---it will reduce clutter.

 

[John86]

That's ok Marcus

John

 

[marcus]

http://arxiv.org/abs/1012.1739
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
6 pages, 1 figure
(Submitted on 8 Dec 2010)
"The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the 'projected' spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity."

http://arxiv.org/abs/1012.1738
Complex Ashtekar variables and reality conditions for Holst's action
Wolfgang Wieland
19 pages, 2 pictures
(Submitted on 8 Dec 2010)
"From the Holst action in terms of complex valued Ashtekar variables additional reality conditions mimicking the linear simplicity constraints of spin foam gravity are found. In quantum theory with the results of You and Rovelli we are able to implement these constraints weakly, that is in the sense of Gupta and Bleuler. The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our result perfectly fit with recent developments of Rovelli and Speziale concerning Lorentz covariance within spin-form gravity."

 

[marcus]

http://arxiv.org/abs/1012.1982
The kinematical Hilbert space of Loop Quantum Gravity from BF theories
Francesco Cianfrani
5 pages
(Submitted on 9 Dec 2010)
"In this work, it is demonstrated how the kinematical Hilbert space of BF theories can be reduced to the one of Loop Quantum Gravity via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints. Then, the reduction to SU(2) intertwiners at vertices takes place by virtue of the vanishing behavior of the momenta associated to the boost parameters."

 

[marcus]

http://arxiv.org/abs/1012.2324
Matter in inhomogeneous loop quantum cosmology: the Gowdy T³ model
Mercedes Martín-Benito, Daniel Martín-de Blas, Guillermo A. Mena Marugán
12 pages, submitted to PRD
(Submitted on 10 Dec 2010)
"We apply a hybrid approach which combines loop and Fock quantizations to fully quantize the linearly polarized Gowdy T³ model in the presence of a massless scalar field with the same symmetries as the metric. Like in the absence of matter content, the application of loop techniques leads to a quantum resolution of the classical cosmological singularity. Most importantly, thanks to the inclusion of matter, the homogeneous sector of the model contains flat Friedmann-Robertson-Walker (FRW) solutions, which are not allowed in vacuo. Therefore, this model provides a simple setting to study at the quantum level interesting physical phenomena such as the effect of the anisotropies and inhomogeneities on flat FRW cosmologies."

 

[marcus]

http://arxiv.org/abs/1012.2776
Vector fields and Loop Quantum Cosmology
Michal Artymowski, Zygmunt Lalak
15 pages, 6 figures
(Submitted on 13 Dec 2010)
"In the context of the Loop Quantum Cosmology we have analysed the holonomy correction to the classical evolution of the simplified Bianchi I model in the presence of vector fields. For the Universe dominated by a massive vector field or by a combination of a scalar field and a vector field a smooth transition between Kasner-like and Kasner-unlike solutions for a Bianchi I model has been demonstrated. In this case a lack of initial singularity and a finite maximal energy density appear already at the level of General Relativity, which simulates a classical Big Bounce."

http://arxiv.org/abs/1012.2419
Multiple quantum collapse of the inflaton field and its implications on the birth of cosmic structure
Gabriel León, Adolfo De Unánue, Daniel Sudarsky
17 pages
(Submitted on 11 Dec 2010)
"The standard inflationary account for the origin of cosmic structure is, without a doubt, extremely successful. However, it is not fully satisfactory as has been argued in [A. Perez, H. Sahlmann, and D. Sudarsky, Class. Quantum Grav., 23, 2317, (2006) arXiv:gr-qc/0508100]. The central point is that, in the standard accounts, the inhomogeneity and anisotropy of our universe seems to emerge, unexplained, from an exactly homogeneous and isotropic initial state through processes that do not break those symmetries. The proposal made there to address this shortcoming calls for a dynamical and self- induced quantum collapse of the original homogeneous and isotropic state of the inflaton. In this article, we consider the possibility of a multiplicity of collapses in each one of the modes of the Quantum Field. As we will see, the results are sensitive to a more detailed characterization of the collapse than those studied in the previous works, and in this regard two simple options will be studied. We find important constraints on the model, most remarkably on the number of possible collapses for each mode."

http://arxiv.org/abs/1012.2680
Planck Scale Cosmology and Asymptotic Safety in Resummed Quantum Gravity
B.F.L. Ward (Department of Physics, Baylor University, Waco, TX)
5 pages; presented by B.F.L. Ward at ICHEP 2010
(Submitted on 13 Dec 2010)
"In Weinberg's asymptotic safety approach, a finite dimensional critical surface for a UV stable fixed point generates a theory of quantum gravity with a finite number of physical parameters. We argue that, in an extension of Feynman's original formulation of the theory, we recover this fixed-point UV behavior from an exact re-arrangement of the respective perturbative series. Our results are consistent with the exact field space Wilsonian renormalization group results of Reuter et al. and with recent Hopf-algebraic Dyson-Schwinger renormalization theory results of Kreimer. We obtain the first "first principles" predictions of the dimensionless gravitational and cosmological constants and our results support the Planck scale cosmology of Bonanno and Reuter. We conclude with an estimate for the currently observed value of the cosmological constant."

 

[marcus]

http://arXiv.org/abs/1012.1798
Generalization of the Bollobás-Riordan polynomial for tensor graphs
Adrian Tanasa
17 pages, 12 figures
(Submitted on 8 Dec 2010)
"Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial T encoding the supplementary topological information. This polynomial is a natural generalization of the Bollobás-Riordan polynomial (used to characterize matrix graphs) and is different of the Gurau polynomial, (R. Gurau, "Topological Graph Polynomials in Colored Group Field Theory", Annales Henri Poincaré 11, 565-584 (2010)) defined for a particular class of tensor graphs, the colorable ones. The polynomial T is defined for both colorable and non-colorable graphs and it is proved to satisfy the contraction/deletion relation. A non-trivial example of a non-colorable graphs is analyzed."

This comes to qg by way of group field theory. A large proportion of the cited references are to Loop-and-allied papers. Despite this, I am not sure how it fits in with LQG--just guessing that it does.

 

[marcus]

http://arxiv.org/abs/1012.3081
The Universal RG Machine
Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig
38 pages
(Submitted on 14 Dec 2010)
"Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational beta-functions of the Einstein-Hilbert truncation, demonstrating their background-independence. As an additional result, the heat-kernel coefficients for transverse vectors and transverse-traceless symmetric matrices are computed to second order in the curvature."

 

[marcus]

http://arxiv.org/abs/1012.3713
Quantum Gowdy model within the new loop quantum cosmology improved dynamics
M Martín-Benito, L J Garay, G A Mena Marugán
4 pages, jpconf.cls, to appear in Proceedings of Spanish Relativity Meeting 2010 (ERE 2010) held in Granada, Spain
(Submitted on 16 Dec 2010)
The linearly polarized Gowdy T³ model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities."

Westra is a former PhD student of Renate Loll at Utrecht, with research in CDT
http://arxiv.org/abs/1012.3472
Localization of particles in quantum field theory
W. Westra
23 pages
(Submitted on 15 Dec 2010)
"We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is difficult if particle localization is defined using the Newton-Wigner position operator as it is non-local and non-covariant. An alternative bilinear covariant position operator is discussed which incorporates a time operator that can be exponentiated to a unitary operator. Moreover, it satisfies an algebra that unifies special relativity and quantum mechanics and has the same form for particles with spin. Higher power position operators are derived which yield Heisenberg's uncertainty relations. Our ideas are illustrated with a relativistic wave function whose probability density can be perfectly localized."

http://arxiv.org/abs/1012.3473
A Causal Alternative to Feynman's Propagator
Jurjen F. Koksma, W. Westra
31 pages, 3 figures
(Submitted on 15 Dec 2010)
"The Feynman propagator used in the conventional in-out formalism in quantum field theory is not a causal propagator as wave packets are propagated virtually instantaneously outside the causal region of the initial state. We formulate a causal in-out formalism in quantum field theory by making use of the Wheeler propagator, the time ordered commutator propagator, which is manifestly causal. Only free scalar field theories and their first quantization are considered. We identify the real Klein Gordon field itself as the wave function of a neutral spinless relativistic particle. Furthermore, we derive a probability density for our relativistic wave packet using the inner product between states that live on a suitably defined Hilbert space of real quantum fields. We show that the time evolution of our probability density is governed by the Wheeler propagator, such that it behaves causally too."

http://arxiv.org/abs/1012.3629
From Quantum Deformations of Relativistic Symmetries to Modified Kinematics and Dynamics
Jerzy Lukierski
29 pages, 1 fig. Invited talk at 50-th Cracow School of Theoretical Physics "Particle Physics at the Dawn of the LHC'', Zakopane, Poland (June 9-19, 2010). To be published in Acta Physica Polonica-B.
(Submitted on 16 Dec 2010)
"We present a short review describing the use of noncommutative space-time in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their realizations (noncommutative modules) as important mathematical tool describing quantum-deformed symmetries: quantum Lie groups and quantum Lie algebras. We consider in some detail the most studied examples of noncommutative space-time geometry: the canonical and kappa-deformed cases. Finally we briefly describe the modifications of Einstein gravity obtained by introduction of noncommutative space-time coordinates."


Brief mention:
http://arxiv.org/abs/1012.3744
Testing the Gaussianity and Statistical Isotropy of the Universe
Dragan Huterer, Sarah Shandera, Eiichiro Komatsu
(Submitted on 16 Dec 2010)
"The last few years have seen a surge in excitement about measurements of statistics of the primordial fluctuations beyond the power spectrum. New ideas for precision tests of Gaussianity and statistical isotropy in the data are developing simultaneously with proposals for a wide range of new theoretical possibilities. From both the observations and theory, it has become clear that there is a huge discovery potential from upcoming measurements. In this Special Issue of Advances in Astronomy we have collected articles that summarize the theoretical predictions for departures from Gaussianity or statistical isotropy from a variety of potential sources, together with the observational approaches to test these properties using the CMB or large-scale structure..."

 

[John86]

http://arxiv.org/abs/1012.3701
Decoherence in Quantum Mechanics
Authors: Jurjen F. Koksma, Tomislav Prokopec, Michael G. Schmidt
(Submitted on 16 Dec 2010)
Abstract: We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system's total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.

 

[Kevin_Axion]

Sorry about that, it must have slipped my eye.

 

[marcus]

Kevin, thanks for deleting the duplicates!

http://arxiv.org/abs/1012.3832
U(N) invariant dynamics for a simplified Loop Quantum Gravity model
Enrique F. Borja, Jacobo Díaz-Polo, Iñaki Garay, Etera R. Livine
4 pages, to appear in Proceedings of Spanish Relativity Meeting 2010 (ERE 2010) held in Granada
(Submitted on 17 Dec 2010)
"The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology."

 

[marcus]

http://arxiv.org/abs/1012.4216
4-dimensional Spin-foam Model with Quantum Lorentz Group
Muxin Han
22 pages, 3 figures
(Submitted on 19 Dec 2010)
"We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model so defined is free of the infrared divergence, thus gives a finite partition function on a fixed triangulation. We expect this quantum group spin-foam model is a spin-foam quantization of discrete gravity with a cosmological constant."

http://arxiv.org/abs/1012.4280
Renormalization Group Flow of the Holst Action
J.-E. Daum, M.Reuter
11 pages, 3 figures
(Submitted on 20 Dec 2010)
"The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way."

 

[marcus]

http://arxiv.org/abs/1012.4707
Loop quantum gravity: the first twenty five years
Carlo Rovelli
24 pages, 3 figures
(Submitted on 21 Dec 2010)
"This is a review paper invited by the journal 'Classical ad Quantum Gravity' for a 'Cluster Issue' on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits."

http://arxiv.org/abs/1012.4719
Spinfoam fermions
Eugenio Bianchi, Muxin Han, Elena Magliaro, Claudio Perini, Carlo Rovelli, Wolfgang Wieland
8 pages
(Submitted on 21 Dec 2010)
"We describe a minimal coupling of fermions and Yang Mills fields to the loop quantum gravity dynamics. The coupling takes a very simple form."

http://arxiv.org/abs/1012.4476
Lessons from Classical Gravity about the Quantum Structure of Spacetime
T. Padmanabhan
Expanded version of the lectures given on several ocassions including (i) Plenary talk at ERE 2010, Granada, September 2010; (ii) Keynote address at DICE 2010, Castiglioncello, September 2010; (iii) Special Lecture at the Indian Academy of Sciences, Bangalore, July 2010
(Submitted on 20 Dec 2010)
"I present the theoretical evidence which suggests that gravity is an emergent phenomenon like gas dynamics or elasticity with the gravitational field equations having the same status as, say, the equations of fluid dynamics/elasticity. This paradigm views a wide class of gravitational theories - including Einstein's theory - as describing the thermodynamic limit of the statistical mechanics of 'atoms of spacetime'. The evidence for this paradigm is hidden in several classical features of the gravitational theories and depends on just one quantum mechanical input, viz. the existence of Davies-Unruh temperature of horizons. I discuss several conceptual ingredients of this approach."

http://arxiv.org/abs/1012.4784
Quantum deformation of two four-dimensional spin foam models
Winston J. Fairbairn, Catherine Meusburger
38 pages, 3 figures
(Submitted on 21 Dec 2010)
"We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian EPRL model. The q-deformed models are based on the representation theory of two copies of U_q(su(2)) at a root of unity and on the quantum Lorentz group with a real deformation parameter. For both models we give a definition of the quantum EPRL intertwiners, study their convergence and braiding properties and construct an amplitude for the four-simplexes. We find that both of the resulting models are convergent."

Brief mention (Classical, not QG):
http://arxiv.org/abs/1012.4467
The causal structure of spacetime is a parameterized Randers geometry
Jozef Skakala (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)
8 pages
(Submitted on 20 Dec 2010)
"There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes - the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (time-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure."

 

[marcus]

Some loop researchers experiment here with applying LQG method (among other things) to string.
http://arxiv.org/abs/1012.5073
Equivalence of the self-dual and Nambu-Goto strings
Winston J. Fairbairn, Karim Noui, Francesco Sardelli
20 pages
(Submitted on 22 Dec 2010)
"We establish explicitly the relation between the algebraic and Nambu-Goto strings when the target space is a four dimensional flat space. We find that the two theories are exactly equivalent only when the algebraic string is restricted to the self-dual or anti self-dual sectors. In its Hamiltonian formulation, the algebraic string defines a constrained system with first and second class constraints. In the self-dual case, we exhibit the appropriate set of second class constraints such that the resulting physical phase space is formulated in the same way as it is in the standard Nambu-Goto string. We conclude with a discussion on alternative quantisation schemes."

Thiemann tried some Lqg-string investigation back around 2004. They cite him and also a bunch of regular Lqg papers (Ashtekar Baez Perez Oriti and others...). They treat a case with no extra dimensions. Could just be a curiosity.

 

[marcus]

http://arxiv.org/abs/1012.5421
Ideal Gas in a strong Gravitational field: Area dependence of Entropy
Sanved Kolekar, T. Padmanabhan
18 pages
(Submitted on 24 Dec 2010)
"We study the thermodynamic parameters like entropy, energy etc. of a box of gas made up of indistinguishable particles when the box is kept in various static background spacetimes having a horizon. We compute the thermodynamic variables using both statistical mechanics as well as by solving the hydrodynamical equations for the system. When the box is far away from the horizon, the entropy of the gas depends on the volume of the box except for small corrections due to background geometry. As the box is moved closer to the horizon with one (leading) edge of the box at about Planck length (L_p) away from the horizon, the entropy shows an area dependence rather than a volume dependence. More precisely, it depends on a small volume A*L_p/2 of the box, upto an order O(L_p/K)² where A is the transverse area of the box and K is the (proper) longitudinal size of the box related to the distance between leading and trailing edge in the vertical direction (i.e in the direction of the gravitational field). Thus the contribution to the entropy comes from only a fraction O(L_p/K) of the matter degrees of freedom and the rest are suppressed when the box approaches the horizon. Near the horizon all the thermodynamical quantities behave as though the box of gas has a volume A*L_p/2 and is kept in a Minkowski spacetime. These effects are: (i) purely kinematic in their origin and are independent of the spacetime curvature (in the sense that Rindler approximation of the metric near the horizon can reproduce the results) and (ii) observer dependent. When the equilibrium temperature of the gas is taken to be equal to the the horizon temperature, we get the familiar A/L_p² dependence in the expression for entropy. All these results hold in a D+1 dimensional spherically symmetric spacetime."

 

[marcus]

I vaguely remember this guy posting at PF Beyond forum some time ago.
The paper is not directly related to QG but want to give brief mention anyway. We feature Asymptotic Safety, don't we?

http://arxiv.org/abs/1012.5529
Asymptotically safe weak interactions
Xavier Calmet
(Submitted on 26 Dec 2010)
"We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a dressing field and might not exist as a propagating particle. In that interpretation, the electroweak interactions without a Higgs boson could be renormalizable at the non-perturbative level because of a non-trivial fixed point. Tree-level unitarity in electroweak bosons scattering is restored by the running of the weak scale."

Happy New Year All!

 

[marcus]

http://arxiv.org/abs/1101.0590
Diffeomorphisms in group field theories
Aristide Baratin, Florian Girelli, Daniele Oriti
31 pages, many figures
(Submitted on 3 Jan 2011)
"We study the issue of diffeomorphism symmetry in group field theories (GFT), using the recently introduced noncommutative metric representation. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j-symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher dimensional BF theories and discuss various insights that they provide on the GFT formalism itself."

http://arxiv.org/abs/1101.0367
Observables in the General Boundary Formulation
Robert Oeckl (UNAM)
20 pages, contribution to the proceedings of the conference "Quantum Field Theory and Gravity" (Regensburg, 2010)
(Submitted on 1 Jan 2011)
"We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like axiomatic structure of the general boundary formulation. We also provide a proposal for a generalized concept of expectation value adapted to this type of observable. We show how the standard notion of quantum observable arises as a special case together with the usual expectation values. We proceed to introduce various quantization schemes to obtain such quantum observables including path integral quantization (yielding the time-ordered product), Berezin-Toeplitz (antinormal ordered) quantization and normal ordered quantization and discuss some of their properties."
20 pages, contribution to the proceedings of the conference "Quantum Field Theory and Gravity" (Regensburg, 2010)


Brief mention:
http://arxiv.org/abs/1101.0389
Cosmological Big Bounce Transition
Wlodzimierz Piechocki
(Submitted on 2 Jan 2011)
9 pages, talk presented at the 11th international symposium `Frontiers of Fundamental Physics [FFP11]', 6-9 July, 2010, Paris, France; to be published in the AIP Conference Proceedings Series
"We analyze the big bounce transition of the quantum FRW model in the setting of the nonstandard loop quantum cosmology (LQC). Elementary observables are used to quantize compound observables. The spectrum of the energy density operator is bounded and continuous. The spectrum of the volume operator is bounded from below and discrete. It has equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of spacetime at semiclassical level which may be detected in astro-cosmo observations. The nonstandard LQC method has a free parameter that should be fixed in some way to specify the big bounce transition."

 

[MTd2]

I think it was posted before, but this version, including the results, are completely changed! ENJOY!

http://arxiv.org/abs/1006.2230v2

On the geometrization of matter by exotic smoothness

Torsten Asselmeyer-Maluga, Helge Rose
(Submitted on 11 Jun 2010 (v1), last revised 4 Jan 2011 (this version, v2))
In this paper we will discuss the question how matter emerges from space. For that purpose we consider the smoothness structure as underlying structure of the spacetime manifold. The smoothness structure depends on an infinite structure -- the Casson handle -- representing the failure to smoothly embed a disc without self-intersections (immersed disc). By using the Weierstrass representation, we are able to show that the immersed discs are represented by spinors fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. Between the immersed discs, there are "connecting tubes" which are realized by an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components of the Casson handle. We also discuss the gauge group of the theory.Comments: 22 pages, no figures, elsevier style, many changes according to the referee's, thanks to Ashtekar for the argumentation about the boundary terms, argumentation about gauge group added

 

[marcus]

Brief mention. In spite of the title, this paper is not solely about string theory. It compares and contrasts a number of different approaches to QG---discussing general problems faced by all, and the state of present knowledge. The author is at the University of Giessen, at the Institute for Philosophy of Science:
http://arxiv.org/abs/1101.0690
String Theory - Nomological Unification and the Epicycles of the Quantum Field Theory Paradigm
Reiner Hedrich
23 pages

 

[marcus]

http://arxiv.org/abs/1101.0931
The principle of relative locality
Giovanni Amelino-Camelia, Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin
12 pages, 3 figures
(Submitted on 5 Jan 2011)
"We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them.
This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature."

 

[MTd2]

http://arxiv.org/abs/1101.1081

General Covariance in Gravity at a Lifgarbagez Point

Petr Horava
(Submitted on 5 Jan 2011)
This paper is based on the invited talks delivered by the author at GR 19: the 19th International Conference on General Relativity and Gravitation, Ciudad de M\'exico, M\'exico, July 2010. In Part 1, we briefly review some of the main features of quantum gravity with anisotropic scaling, and comment on its possible relation to the causal dynamical triangulations (CDT) approach to lattice quantum gravity. Part 2 explains the construction of gravity with anisotropic scaling with an extended gauge symmetry -- essentially a nonrelativistic version of general covariance. This extra symmetry eliminates the scalar graviton polarization, and thus brings the theory closer to general relativity at long distances.

 

[MTd2]

http://arxiv.org/abs/1101.1424

On Gravity, Torsion and the Spectral Action Principle

Frank Pfaeffle, Christoph A. Stephan
(Submitted on 7 Jan 2011)
We consider closed Riemannian spin manifolds with orthogonal connections. We regard the induced Dirac operators and the associated commutative spectral triples. In case of dimension four we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.

Marcus deleted, but I will post!

http://arxiv.org/abs/1101.1417
Canonical Relational Quantum Mechanics from Information Theory

Joakim Munkhammar
(Submitted on 7 Jan 2011)
In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.

 

[marcus]

http://arxiv.org/abs/1101.1615
A taste of Hamiltonian constraint in spin foam models
Valentin Bonzom
16 pages
(Submitted on 8 Jan 2011)
"The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known to display rapid oscillations whose frequency is the Regge action. In this note, we reformulate this result through a difference equation, asymptotically satisfied by these models, and whose semi-classical solutions are precisely the sine and the cosine of the Regge action. This equation is then interpreted as coming from the canonical quantization of a simple constraint in Regge calculus. This suggests to lift and generalize this constraint to the phase space of loop quantum gravity parametrized by twisted geometries. The result is a reformulation of the flat model for topological BF theory from the Hamiltonian perspective. The Wheeler-de-Witt equation in the spin network basis gives difference equations which are exactly recursion relations on the 15j-symbol. Moreover, the semi-classical limit is investigated using coherent states, and produces the expected results. It mimics the classical constraint with quantized areas, and for Regge geometries it reduces to the semi-classical equation which has been introduced in the beginning."

http://arxiv.org/abs/1101.1690
Chern-Simons theory, Stokes' Theorem, and the Duflo map
Hanno Sahlmann, Thomas Thiemann
26 pages, 8 figures
(Submitted on 10 Jan 2011)
"We consider a novel derivation of the expectation values of holonomies in Chern-Simons theory, based on Stokes' Theorem and the functional properties of the Chern-Simons action. It involves replacing the connection by certain functional derivatives under the path integral integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity."

http://arxiv.org/abs/1101.1738
Loop Quantum Cosmology: A cosmological theory with a view
Guillermo A. Mena Marugan
17 pages, to appear in Proceedings of Spanish Relativity Meeting 2010 (ERE 2010) held in Granada, Spain
(Submitted on 10 Jan 2011)
"Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and exciting views of the gravitational phenomena that took place in the early universe, or that occur in spacetime regions where Einstein's theory predicts singularities. We provide a brief introduction to the bases of Loop Quantum Cosmology and summarize the most important results obtained in homogeneous scenarios. These results include a mechanism to avoid the cosmological Big Bang singularity and replace it with a Big Bounce, as well as the existence of processes which favor inflation. We also discuss the extension of the frame of Loop Quantum Cosmology to inhomogeneous settings."

http://arxiv.org/abs/1101.1752
Extension of loop quantum gravity to f(R) theories
Xiangdong Zhang, Yongge Ma
4 pages
(Submitted on 10 Jan 2011)
"The 4-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real SU(2)-connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the non-perturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity."

 

[marcus]

http://arxiv.org/abs/1101.2174
Cosmology within Noncommutative Spectral Geometry
Mairi Sakellariadou
14 pages. Invited talk in the Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity, September 8-12, 2010 Corfu Greece
(Submitted on 11 Jan 2011)
"Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum gravity theory, one may follow an effective approach and consider space-time as the product of a four-dimensional continuum compact Riemanian manifold by a tiny discrete finite noncommutative space. Since all available data are of a spectral nature, one may argue that it is more appropriate to apply the spectral action principle in this almost commutative space. Following this procedure one obtains an elegant geometric explanation for the most successful particle physics model, namely the standard model (and supersymmetric extensions) of electroweak and strong interactions in all its details, as determined by experimental data. Moreover, since this gravitational theory lives by construction at very high energy scales, it offers a perfect framework to address some of the early universe cosmological questions still awaiting for an answer.
After introducing some of the main mathematical elements of noncommutative spectral geometry, I will discuss various cosmological and phenomenological consequences of this theory, focusing in particular on constraints imposed on the gravitational sector of the theory."

Brief mention:
http://arxiv.org/abs/1101.2186
Making the Case for Conformal Gravity
Philip D. Mannheim
30 pages, 20 figures. Presentation at the International Conference on Two Cosmological Models, Universidad Iberoamericana, Mexico City, November 17-19, 2010.
(Submitted on 11 Jan 2011)
"We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source...
...We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 110 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever...
...Finally, we review some recent work by 't Hooft in which a connection between conformal gravity and Einstein gravity has been found."

 

[marcus]

For connection to LQG and Loop cosmology, see page 10 and following.
http://arxiv.org/abs/1101.2397
Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes
Jeronimo Cortez, Guillermo A. Mena Marugan, Javier Olmedo, Jose M. Velhinho
(Submitted on 12 Jan 2011)
"The Fock quantization of fields propagating in cosmological spacetimes is not uniquely determined because of several reasons. Apart from the ambiguity in the choice of the quantum representation of the canonical commutation relations, there also exists certain freedom in the choice of field: one can scale it arbitrarily absorbing background functions, which are spatially homogeneous but depend on time. Each nontrivial scaling turns out into a different dynamics and, in general, into an inequivalent quantum field theory. In this work we analyze this freedom at the quantum level for a scalar field in a nonstationary, homogeneous spacetime whose spatial sections have S³ topology. A scaling of the configuration variable is introduced as part of a linear, time dependent canonical transformation in phase space. In this context, we prove in full detail a uniqueness result about the Fock quantization requiring that the dynamics be unitary and the spatial symmetries of the field equations have a natural unitary implementation. The main conclusion is that, with those requirements, only one particular canonical transformation is allowed, and thus only one choice of field-momentum pair (up to irrelevant constant scalings). This complements another previous uniqueness result for scalar fields with a time varying mass on S³, which selects a specific equivalence class of Fock representations of the canonical commutation relations under the conditions of a unitary evolution and the invariance of the vacuum under the background symmetries. In total, the combination of these two different statements of uniqueness picks up a unique Fock quantization for the system. We also extend our proof of uniqueness to other compact topologies and spacetime dimensions."

 

[atyy]

http://arxiv.org/abs/1101.1958
What Really Sets the Upper Bound on Quantum Correlations?Joy Christian (Oxford)
(Submitted on 10 Jan 2011)
The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible torsion within all norm-composing parallelizable manifolds. A profound interplay is thus uncovered between the existence and strength of quantum correlations and the parallelizability of the spheres S^0, S^1, S^3, and S^7 necessitated by the four real division algebras. In particular, parallelization within a unit 3-sphere is shown to be responsible for the existence of EPR and Hardy type correlations, whereas that within a unit 7-sphere is shown to be responsible for the existence of all GHZ type correlations. Moreover, parallelizability in general is shown to be equivalent to the completeness criterion of EPR, in addition to necessitating the locality condition of Bell. It is therefore shown to predetermine both the local outcomes as well as the quantum correlations among the remote outcomes, dictated by the infinite factorizability of points within the spheres S^3 and S^7. The twin illusions of quantum entanglement and non-locality are thus shown to stem from the topologically incomplete accountings of the measurement results.

 

[PhilKravitz]

in classical mechanics things move along trajectories---curved paths parametrized by time---and when you quantize the trajectories go away.

the curved paths things travel along don't exist any more, you have to erase the trajectories (or in Feynman sum over histories you "integrate" all possible ways of getting from here to there---in any case the clear picture of a path loses reality and dissipates)

It seems to me more like Feynmann's sum over paths changes not at all with a network of discrete paths. It is still the sum over all possible paths. The classical trajectory is now more like diffusion along the discrete edges of the mesh.

 

[marcus]

Phil,
please do start a separate thread for discussion of the topic you have in mind. This thread began back in 2003 with some discussion, but quickly evolved into a bibliography. It is no longer used for discussion. It's sole function now is to list current QG research articles: Loop-and-allied quantum gravity.
Mixing in discussion of various topics would dilute the thread and make it less usable as a bibliography.

 

[atyy]

http://arxiv.org/abs/1101.2451
From Navier-Stokes To Einstein
Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, Andrew Strominger
(Submitted on 12 Jan 2011)
We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p+1 dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in p+2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For p=2, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence.

 

[marcus]

http://arxiv.org/abs/1101.2744
Time in quantum gravity and black-hole information paradox
Harvey Nikolic
(Submitted on 14 Jan 2011)
"The fact that canonical quantum gravity does not possesses a fundamental notion of time implies that the theory is unitary in a trivial sense. At the fundamental level, this trivial unitarity leaves no room for a black-hole information loss. Yet, a phenomenological loss of information may appear when some matter degrees of freedom are reinterpreted as a clock-time. This explains how both fundamental unitarity and phenomenological information loss may peacefully coexist, which offers a resolution of the black-hole information paradox."

http://arxiv.org/abs/1101.2841
Palatini Actions and Quantum Gravity Phenomenology
Gonzalo J. Olmo
7 pages, 1 figure
(Submitted on 14 Jan 2011)
"We show that a quadratic gravitational Lagrangian in the Palatini formulation is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, we show that in this theory field excitations propagating with different energy-densities perceive different background metrics, which is a fundamental characteristic of the DSR and Rainbow Gravity approaches. Also, the resulting isotropic and anisotropic cosmologies are free from the big bang singularity. This singularity avoidance occurs non-perturbatively and shares some similitudes with the effective dynamics of loop quantum cosmology."

 

[marcus]

http://arxiv.org/abs/1101.3264
Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
Muxin Han, Carlo Rovelli
26 pages, 9 figures
(Submitted on 17 Jan 2011)
"We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravity-fermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved for spinfoam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spinfoams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex."

http://arxiv.org/abs/1101.3294
Finiteness of the EPRL/FK spin foam model
Aleksandar Mikovic, Marko Vojinovic
(Submitted on 17 Jan 2011)
"We show that the EPRL/FK spin foam model of quantum gravity can be made finite by dividing the vertex amplitude with an appropriate power p of the product of dimensions of the vertex spins and intertwiners. This power is independent of the spin foam and we find a lower bound for p which makes the state sum absolutely convergent."

http://arxiv.org/abs/1101.3151
Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds
Shahar Hod
6 pages
(Submitted on 17 Jan 2011)
Bekenstein has presented evidence for the existence of a universal upper bound of magnitude 2 pi R/hbarc to the entropy-to-energy ratio S/E of an arbitrary three dimensional system of proper radius R and negligible self-gravity. In this paper we derive a generalized upper bound on the entropy-to-energy ratio of a (D+1)-dimensional system. We consider a box full of entropy lowered towards and then dropped into a (D+1)-dimensional black hole in equilibrium with thermal radiation. In the canonical case of three spatial dimensions, it was previously established that due to quantum buoyancy effects the box floats at some neutral point very close to the horizon. We find here that the significance of quantum buoyancy increases dramatically with the number D of spatial dimensions. In particular, we find that the neutral (floating) point of the box lies near the horizon only if its length b is large enough such that b/b_C>F(D), where b_C is the Compton length of the body and F(D) ~ D^D/2 >> 1 for D >> 1. A consequence is that quantum buoyancy severely restricts our ability to deduce the universal entropy bound from the generalized second law of thermodynamics in higher-dimensional spacetimes with D >> 1. Nevertheless, we find that the universal entropy bound is always a sufficient condition for operation of the generalized second law in this type of gedanken experiments."

http://arxiv.org/abs/1101.3168
Gravitational sources induced by exotic smoothness
T. Asselmeyer-Maluga, C.H. Brans
17 pages, 8 figures, 5 appendices
(Submitted on 17 Jan 2011)
"In this paper we construct a coordinate atlas in an exotic R⁴ using Bizaca's construction. The main source for such an atlas is the handle body decomposition of a Casson handle, which of course is an infinite, but periodic, process. The immersion of the end-periodic manifold into R⁴ is directly related to the exoticness of the R⁴ and also gives rise naturally to a spinor field. Thus we obtain the interesting result that the simplest exotic R⁴ generates an extra spinor field by exoticness."

αβγδεζηθικλμνξοπρσςτυφχψωΓΔΘΛΞΠΣΦΨΩ∏∑∫∂√±←↓→↑↔~≈≠≡ ≤≥½∞(⇐⇑⇒⇓⇔∴∃ℝℤℕℂ⋅)
:

 

[MTd2]

http://arxiv.org/abs/1101.3524

The Hamiltonian constraint in 3d Riemannian loop quantum gravity

Valentin Bonzom, Laurent Freidel
(Submitted on 18 Jan 2011)
We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the extrinsic curvature from dihedral angles. The Wheeler-DeWitt equation takes the form of difference equations, which are actually recursion relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the Hamiltonian generates the exact recursion relation on the 6j-symbol which comes from the Biedenharn-Elliott (pentagon) identity. This fills the gap between the canonical quantization and the symmetries of the Ponzano-Regge state-sum model for 3d gravity.

 

[marcus]

http://arxiv.org/abs/1101.3660
Detailed black hole state counting in loop quantum gravity
Ivan Agullo, J. Fernando Barbero G., Enrique F. Borja, Jacobo Diaz-Polo, Eduardo J. S. Villaseñor
Phys.Rev.D82:084029,2010
(Submitted on 19 Jan 2011)
"We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step towards obtaining the behavior of entropy in the asymptotic (large horizon area) regime."

http://arxiv.org/abs/1101.3662
Statistical description of the black hole degeneracy spectrum
J. Fernando Barbero G., Eduardo J. S. Villaseñor
41 pages, 12 figures
(Submitted on 19 Jan 2011)
"We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity."