Loop-and-allied QG bibliography

[marcus]

http://arxiv.org/abs/1302.2810
Four-dimensional Causal Dynamical Triangulations and an effective transfer matrix
Andrzej Görlich
(Submitted on 12 Feb 2013)
Causal Dynamical Triangulations is a background independent approach to quantum gravity. We show that there exists an effective transfer matrix labeled by the scale factor which properly describes the evolution of the quantum universe. In this framework no degrees of freedom are frozen, but, the obtained effective action agrees with the minisuperspace model.
Comments: To appear in the Proceedings of the 13th Marcel Grossmann Meeting on General

 

[John86]

http://arxiv.org/abs/1302.2849
Disappearance and emergence of space and time in quantum gravity
Daniele Oriti
(Submitted on 12 Feb 2013)
We discuss the hints for the disappearance of continuum space and time at microscopic scale. These include arguments for a discrete nature of them or for a fundamental non-locality, in a quantum theory of gravity. We discuss how these ideas are realized in specific quantum gravity approaches. Turning then the problem around, we consider the emergence of continuum space and time from the collective behaviour of discrete, pre-geometric atoms of quantum space, and for understanding spacetime as a kind of "condensate", and we present the case for this emergence process being the result of a phase transition, dubbed "geometrogenesis". We discuss some conceptual issues of this scenario and of the idea of emergent spacetime in general. As a concrete example, we outline the GFT framework for quantum gravity, and illustrate a tentative procedure for the emergence of spacetime in this framework. Last, we re-examine the conceptual issues raised by the emergent spacetime scenario in light of this concrete example.

http://arxiv.org/abs/1302.2850
The universal path integral
Seth Lloyd, Olaf Dreyer
(Submitted on 12 Feb 2013)
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness, together with a method for extracting probabilities for observable quantities. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.

http://arxiv.org/abs/1302.2687
Massive gravity as a limit of bimetric gravity
Prado Martin-Moruno (Victoria University of Wellington), Valentina Baccetti (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)
(Submitted on 12 Feb 2013)
Massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure can lead to an interesting interplay between the "background" and "foreground" metrics in a cosmological context. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit. Thus, solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true.

http://arxiv.org/abs/1302.2731
Quantum correlations which imply causation
Joseph Fitzsimons, Jonathan Jones, Vlatko Vedral
(Submitted on 12 Feb 2013)
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time, in conflict with special relativity where space and time are treated on an equal footing. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix which treats space and time indiscriminately. This matrix in general fails to be positive for timelike separated measurements, motivating us to define a measure of causality that discriminates between spacelike and timelike correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements.

 

[John86]

http://arxiv.org/abs/1302.2928
Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
Alfio Bonanno, Martin Reuter
(Submitted on 12 Feb 2013)
We discuss the stabilization of the conformal factor by higher derivative terms in a conformally reduced $R+R^2$ Euclidean gravity theory. The flat spacetime is unstable towards the condensation of modes with nonzero momentum, and they "condense" in a modulated phase above a critical value of the coupling $\beta$ of the $R^2$ term. By employing a combination of variational, numerical and lattice methods we show that in the semiclassical limit the corresponding functional integral is dominated by a single nonlinear plane wave of frequency $\approx 1/\sqrt{\beta} \lp$. We argue that the ground state of the theory is characterized by a spontaneous breaking of translational invariance at Planckian scales.

 

[marcus]

http://arxiv.org/abs/1302.3226
Solution to the cosmological constant problem
T. Padmanabhan, Hamsa Padmanabhan
(Submitted on 13 Feb 2013)
The current, accelerated, phase of expansion of our universe can be modeled in terms of a cosmological constant. A key issue in theoretical physics is to explain the extremely small value of the dimensionless parameter Λ L_P² ~ 3.4 x 10^-122, where L_P is the Planck length. We show that this value can be understood in terms of a new dimensionless parameter N, which counts the number of modes inside a Hubble volume crossing the Hubble radius, from the end of inflation until the beginning of the accelerating phase. Theoretical considerations suggest that N = 4π. On the other hand, N is related to ln(ΛL_P²) and two other parameters which will be determined by high energy particle physics: (a) the ratio between the number densities of photons and matter and (b) the energy scale of inflation. For realistic values of (n_γ/n_m) ~ 4.3 x 10¹⁰ and E_inf ~ 10¹⁵ GeV, our postulate N =4π leads to the observed value of the cosmological constant. This provides a unified picture of cosmic evolution relating the early inflationary phase to the late accelerating phase.
15 pages; 2 figures

 

[MTd2]

http://arxiv.org/abs/1302.3406

Spontaneous Lorentz Violation in Gauge Theories

A. P. Balachandran, S. Vaidya
(Submitted on 14 Feb 2013)
Frohlich, Morchio and Strocchi long ago proved that Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected "Sky" group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.

 

[marcus]

http://arxiv.org/abs/1302.3833
Loop Quantum Cosmology
Ivan Agullo, Alejandro Corichi
(Submitted on 15 Feb 2013)
This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of effective equations that incorporate the main quantum corrections to the dynamics. We also summarize the theory of quantized metric perturbations propagating in those quantum backgrounds. Finally, we describe how this framework can be applied to obtain a self-consistent extension of the inflationary scenario to incorporate quantum aspects of gravity, and to explore possible phenomenological consequences.
52 pages, 5 figures. To appear as a Chapter of "The Springer Handbook of Spacetime," edited by A. Ashtekar and V. Petkov. (Springer-Verlag, at Press).

 

[John86]

http://arxiv.org/abs/1302.1496
Standard Model Higgs field and energy scale of gravity
F.R. Klinkhamer
(Submitted on 6 Feb 2013 (v1), last revised 14 Feb 2013 (this version, v3))
The effective potential of the Higgs scalar field in the Standard Model may have a second degenerate minimum at an ultrahigh vacuum expectation value. This second minimum then determines, by radiative corrections, the values of the top-quark and Higgs-boson masses at the standard minimum corresponding to the electroweak energy scale. An argument is presented that this ultrahigh vacuum expectation value is proportional to the energy scale of gravity, E_{Planck} \equiv \sqrt{\hbar c^5/G_N}, considered to be characteristic of a spacetime foam. In the context of a simple model, the existence of kink-type wormhole solutions places a lower bound on the ultrahigh vacuum expectation value and this lower bound is of the order of E_{Planck}.

http://arxiv.org/abs/1302.3680
Quantum Gravity on a Quantum Computer?
Achim Kempf
(Submitted on 15 Feb 2013)
EPR-type measurements on spatially separated entangled spin qubits allow one, in principle, to detect curvature. Also the entanglement of the vacuum state is affected by curvature. Here, we ask if the curvature of spacetime can be expressed entirely in terms of the spatial entanglement structure of the vacuum. This would open up the prospect that quantum gravity could be simulated on a quantum computer and that quantum information techniques could be fully employed in the study of quantum gravity.

http://arxiv.org/abs/1302.3648
Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
A. del Campo, T. W. B. Kibble, W. H. Zurek
(Submitted on 14 Feb 2013)
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: It obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental test of defect formation theories.

 

[marcus]

http://arxiv.org/abs/1302.5265
The loop quantum gravity black hole
Rodolfo Gambini, Jorge Pullin
(Submitted on 21 Feb 2013)
We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian and therefore the constraint algebra is a true Lie algebra. This allows the completion of the Dirac quantization procedure using loop quantum gravity techniques. We can construct explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. New observables living in the bulk appear at the quantum level (analogous to spin in quantum mechanics) that are not present at the classical level and are associated with the discrete nature of the spin network states of loop quantum gravity. The resulting quantum space-times resolve the singularity present in the classical theory inside black holes. The new observables that arise suggest a possible resolution for the "firewall" problem of evaporating black holes.
Comments: 4 pages,

 

[MTd2]

http://arxiv.org/abs/1302.5273

There exist no 4-dimensional geodesically equivalent metrics with the same stress-energy tensor

Volodymir Kiosak, Vladimir S. Matveev
(Submitted on 21 Feb 2013)
We show that if two 4-dimensional metrics of arbitrary signature on one manifold are geodesically equivalent (i.e., have the same geodesics considered as unparameterized curves) and are solutions of the Einstein field equation with the same stress-energy tensor, then they are affinely equivalent or flat. Under the additional assumption that the metrics are complete or the manifold is closed, the result survives in all dimensions >2.

http://arxiv.org/abs/1302.5162

On CCC-predicted concentric low-variance circles in the CMB sky

V. G. Gurzadyan, R. Penrose
(Submitted on 21 Feb 2013)
A new analysis of the CMB, using WMAP data, supports earlier indications of non-Gaussian features of concentric circles of low temperature variance. Conformal cyclic cosmology (CCC) predicts such features from supermassive black-hole encounters in an aeon preceding our Big Bang. The significance of individual low-variance circles in the true data has been disputed; yet a recent independent analysis has confirmed CCC's expectation that CMB circles have a non-Gaussian temperature distribution. Here we examine concentric sets of low-variance circular rings in the WMAP data, finding a highly non-isotropic distribution. A new "sky-twist" procedure, directly analysing WMAP data, without appeal to simulations, shows that the prevalence of these concentric sets depends on the rings being circular, rather than even slightly elliptical, numbers dropping off dramatically with increasing ellipticity. This is consistent with CCC's expectations; so also is the crucial fact that whereas some of the rings' radii are found to reach around $15^\circ$, none exceed $20^\circ$. The non-isotropic distribution of the concentric sets may be linked to previously known anomalous and non-Gaussian CMB features.

 

[marcus]

http://arxiv.org/abs/1302.5695
Quantum matter in quantum space-time
Martin Bojowald, Golam Mortuza Hossain, Mikhail Kagan, Casey Tomlin
(Submitted on 22 Feb 2013)
Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time are inapplicable in canonical quantum gravity, even at the level of effective equations.
16 pages

http://arxiv.org/abs/1302.5564
Spin-cube Models of Quantum Gravity
A. Mikovic
(Submitted on 22 Feb 2013)
We study the state-sum models of quantum gravity based on a representation 2-category of the Poincare 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be considered as a path integral for a constrained 2-BF theory, and depending on how the constraints are imposed, a spin-cube state sum can be reduced to a path integral for the area-Regge model with the edge-length constraints, or to a path integral for the Regge model. We also show that the effective actions for these spin-cube models have the correct classical limit.
16 pages

brief mention (Shapo is always interesting):
http://arxiv.org/abs/1302.5619
Spontaneously Broken Conformal Symmetry: Dealing with the Trace Anomaly
Roberta Armillis, Alexander Monin, Mikhail Shaposhnikov
(Submitted on 22 Feb 2013)
The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance. At the same time any realistic theory must contain gravity and is thus non-renormalizable. We show that discarding the renormalizability it is possible to construct viable models allowing to preserve the scale invariance at the quantum level. We present explicit one-loop computations for two toy models to demonstrate the main idea of the approach. Constructing the renormalized energy momentum tensor we show that it is traceless, meaning that the conformal invariance is also preserved.
20 pages, 5 figures

 

[marcus]

http://arxiv.org/abs/1302.6264
The Solution to the Problem of Time in Shape Dynamics
Julian Barbour, Tim Koslowski, Flavio Mercati
(Submitted on 25 Feb 2013)
The absence of unique time evolution in Einstein's spacetime description of gravity leads to the hitherto unresolved 'problem of time' in quantum gravity. Shape Dynamics is an objectively equivalent representation of gravity that trades spacetime refoliation invariance for three-dimensional conformal invariance. Its logical completion presented here gives a dimensionless description of gravitational dynamics. We show that in this framework the classical problem of time is completely solved. Since a comparable definitive solution is impossible within the spacetime description, we believe Shape Dynamics provides a key ingredient for the creation of quantum gravity.
14 pages

http://arxiv.org/abs/1302.6566
Singularity resolution from polymer quantum matter
Andreas Kreienbuehl, Tomasz Pawlowski
(Submitted on 26 Feb 2013)
We study the polymeric nature of quantum matter fields using the example of a Friedmann-Lemaitre-Robertson-Walker universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via deparametrization techniques, with the scale factor playing the role of time. Subsequently the remaining dynamic degrees of freedom are polymer quantized. The analysis of the resulting dynamic shows that the big bang singularity is resolved, although with the form of the resolution differing significantly from that of the models with matter clocks: dynamically, the singularity is made passable rather than avoided. Furthermore, the results of the genuine quantum analysis expose crucial limitations to the so-called effective dynamics in loop quantum cosmology when applied outside of the simplest isotropic settings.
12 pages and 4 figures

 

[marcus]

http://arxiv.org/abs/1302.7142
Holonomy Operator and Quantization Ambiguities on Spinor Space
Etera R. Livine
(Submitted on 28 Feb 2013)
We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant 'generalized ladder operators' recently introduced in the U(N) approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity.
14 pages

http://arxiv.org/abs/1302.7135
Fields and Laplacians on Quantum Geometries
Johannes Thürigen
(Submitted on 28 Feb 2013)
In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.
3 pages, submitted to the Proceedings of the 13th Marcel Grossmann Meeting (MG13), Stockholm, July 1-7, 2012

http://arxiv.org/abs/1302.7037
Loop Quantization of Shape Dynamics
Tim Koslowski
(Submitted on 28 Feb 2013)
Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of the physical Hilbert space for pure quantum gravity. This is due to the complicated nature of the Hamilton constraints. The Shape Dynamics description of General Relativity (GR) replaces the Hamilton constraints with spatial Weyl constraints, so the problem of finding the physical Hilbert space reduces to the problem of quantizing the Weyl constraints. Unfortunately, it turns out that a loop quantization of Weyl constraints is far from trivial despite their intuitive physical interpretation. A tentative quantization proposal and interpretation proposal is given in this contribution.
3 pages, talk given at the 13th Marcel Grossmann Meeting, Stockholm 1-7 July 2012

I don't normally list online seminar talks but these might be of particular interest to people following QG research:
http://pirsa.org/13020132/
Quantum Gravity as Random Geometry
Vincent Rivasseau
Abstract: Matrix models, random maps and Liouville field theory are prime tools which connect random geometry and quantum gravity in two dimensions. The tensor track is a new program to extend this connection to higher dimensions through the corresponding notions of tensor models, colored triangulations and tensor group field theories.
27/02/2013

http://pirsa.org/13020146/
The universe as a process of unique events
Lee Smolin
26/02/2013
(Covers material from a new book "Time Reborn" listed on Amazon to appear April 2013)

also of interest, possibly related:
http://arxiv.org/abs/1302.7291
General Relativity and Quantum Cosmology
The arrow of time and the nature of spacetime
George F R Ellis
(Submitted on 28 Feb 2013)
This paper extends the work of a previous paper [arXiv:1108.5261] on top-down causation and quantum physics, to consider the origin of the arrow of time. It proposes that a `past condition' cascades down from cosmological to micro scales, being realized in many microstructures and setting the arrow of time at the quantum level by top-down causation. This physics arrow of time then propagates up, through underlying emergence of higher level structures, to geology, astronomy, engineering, and biology. The appropriate space-time picture to view all this is an emergent block universe (`EBU'), that recognizes the way the present is different from both the past and the future. This essential difference is the ultimate reason the arrow of time has to be the way it is.
56 pages, 6 figures

 

[marcus]

http://arxiv.org/abs/1303.0195
Living in Curved Momentum Space
J. Kowalski-Glikman
(Submitted on 1 Mar 2013)
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled to particles, when (topological) degrees of freedom of gravity are solved for. We argue that there might exist a similar topological phase of quantum gravity in 3+1 dimensions. Then we characterize the main properties of the theory of interacting particles with curved momentum space and the symmetries of the action. We discuss the spacetime picture and the emergence of the principle of relative locality, according to which locality of events is not absolute but becomes observer dependent, in the controllable, relativistic way. We conclude with the detailed review of the most studied kappa-Poincare framework, which corresponds to the de Sitter momentum space.
23 pages

http://arxiv.org/abs/1303.0196
Inhomogeneous Universe in Loop Quantum Gravity
Francesco Cianfrani
(Submitted on 1 Mar 2013)
It is discussed a truncation of the kinematical Hilbert space of Loop Quantum Gravity, which describes the dynamical system associated with an inhomogeneous cosmological model.
3 pages, contribution to the Proceedings of the 13th Marcel Grossman Meeting (Stockholm, Sweden, July 1-7 2012)

http://arxiv.org/abs/1303.0060
Differences and similarities between Shape Dynamics and General Relativity
Henrique Gomes, Tim Koslowski
(Submitted on 1 Mar 2013)
The purpose of this contribution is to elucidate some of the properties of Shape Dynamics (SD) and is largely based on a recent longer article. We shall point out some of the key differences between SD and related theoretical constructions, illustrate the central mechanism of symmetry trading in electromagnetism and finally point out some new quantization strategies inspired by SD. We refrain from describing mathematical detail and from citing literature. For both we refer to the longer article.
3 pages, talk given at the 13th Marcel Grossmann Meeting in Stockholm, July 2012

http://arxiv.org/abs/1303.0174
MG13 Proceedings: A lattice Universe as a toy-model for inhomogeneous cosmology
Jean-Philippe Bruneton
(Submitted on 1 Mar 2013)
We briefly report on a previously found new, approximate, solution to Einstein field equations, describing a cubic lattice of spherical masses. This model mimics in a satisfactory way a Universe which can be strongly inhomogeneous at small scales, but quite homogeneous at large ones. As a consequence of field equations, the lattice Universe is found to expand or contract in the same way as the solution of a Friedmann Universe filled with dust having the same average density. The study of observables indicates however the possible existence of a fitting problem, i.e. the fact that the Friedmann model obtained from past-lightcone observables does not match with the one obtained by smoothing the matter content of the Universe.
3 pages. Prepared for MG13 conference

 

[John86]

http://arxiv.org/abs/1303.0762
A new perspective on early cosmology
Emanuele Alesci
(Submitted on 4 Mar 2013)
We present a new perspective on early cosmology based on Loop Quantum Gravity. We use projected spinnetworks, coherent states and spinfoam techniques, to implement a quantum reduction of the full Kinematical Hilbert space of LQG, suitable to describe inhomogeneous cosmological models. Some preliminary results on the solutions of the Scalar constraint of the reduced theory are also presented.

http://arxiv.org/abs/1303.0433
A Dynamics for Discrete Quantum Gravity
Stan Gudder
(Submitted on 2 Mar 2013)
This paper is based on the causal set approach to discrete quantum gravity. We first describe a classical sequential growth process (CSGP) in which the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the "completed" universe is given by a path through a discretely growing chain of causets. We then quantize the CSGP by forming a Hilbert space $H$ on the set of paths. The quantum dynamics is governed by a sequence of positive operators $\rho_n$ on $H$ that satisfy normalization and consistency conditions. The pair $(H,\brac{\rho_n})$ is called a quantum sequential growth process (QSGP). We next discuss a concrete realization of a QSGP in terms of a natural quantum action. This gives an amplitude process related to the sum over histories" approach to quantum mechanics. Finally, we briefly discuss a discrete form of Einstein's field equation and speculate how this may be employed to compare the present framework with classical general relativity theory.

 

[marcus]

http://arxiv.org/abs/1303.0752
Inclusion of matter in inhomogeneous loop quantum cosmology
Daniel Martín-de Blas, Mercedes Martín-Benito, Guillermo A. Mena Marugán
(Submitted on 4 Mar 2013)
We study the hybrid quantization of the linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric. For simplicity, we quantize its restriction to the model with local rotational symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the geometry are quantized \`a la loop, leading to the resolution of the cosmological singularity. A Fock quantization is employed both for the matter and the gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction, providing a perfect scenario to study the quantum back-reaction of the inhomogeneities on the polymeric homogeneous and isotropic background.
4 pages

 

[Leucippus]

I told you I would make several false starts. Eventually there should be a non-technical description of loop gravity in only one to ten pages. Let's keep this thread going until we have one, or find one in the literature.

Hi, sorry for the interruption, I quoted the above from post #17 of this thread.

I'm just wondering if a non-technical discussion of loop gravity in only one to ten pages has ever been achieved?

I would love to have a nice concise and refined synopsis of the main ideas of LQG along with perhaps a well-organized outline of what types of topics are most required.

My specific interests in LQG is to try to understand how and why it is 'background independent", and also any information that might be known on how it might relate to the entropy associated with the horizon area of a black hole. Or actually any information on how a spin network itself relates to the concept of entropy.

Thanks.

 

[marcus]

Hi Leucippus, this thread started out with discussion (in 2003) but evolved into a Loop and allied QG bibliography. We can start separate discussion threads. You have some good questions so I gathered excerpts (including from this latest) and started a new thread. I hope the new one will prove satisfactory.
https://www.physicsforums.com/showthread.php?p=4298277&posted=1#post4298277

 

[marcus]

http://arxiv.org/abs/1303.1687
Quantum states of the bouncing universe
Jean Pierre Gazeau, Jakub Mielczarek, Wlodzimierz Piechocki
(Submitted on 7 Mar 2013)
In this paper we study quantum dynamics of the bouncing cosmological model. We focus on the model of the flat Friedman-Robertson-Walker universe with a free scalar field. The bouncing behavior, which replaces classical singularity, appears due to the modification of general relativity along the methods of loop quantum cosmology. We show that there exist a unitary transformation that enables to describe the system as a free particle with Hamiltonian equal to canonical momentum. We examine properties of the various quantum states of the Universe: boxcar state, standard coherent state, and soliton-like state, as well as Schrödinger's cat states constructed from these states. Characteristics of the states such as quantum moments and Wigner functions are investigated. We show that each of these states have, for some range of parameters, a proper semiclassical limit fulfilling the correspondence principle. Decoherence of the superposition of two universes is described and possible interpretations in terms of triad orientation and Belinsky-Khalatnikov-Lifgarbagez conjecture are given. Some interesting features regarding the area of the negative part of the Wigner function have emerged.
18 pages, 19 figures

brief mention:
http://arxiv.org/abs/1303.1535
The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm
Krishnamohan Parattu, Bibhas Ranjan Majhi, T. Padmanabhan
(Submitted on 6 Mar 2013)

http://arxiv.org/abs/1303.1782
Non-Associative Geometry and the Spectral Action Principle
Shane Farnsworth, Latham Boyle
(Submitted on 7 Mar 2013)
Chamseddine and Connes have shown how the action for Einstein gravity, coupled to the SU(3) × SU(2) × U(1) standard model of particle physics, may be elegantly recast as the "spectral action" on a certain "non-commutative geometry." In this paper, we show how this formalism may be extended to "non-associative geometries," and explain the motivations for doing so. As a guiding illustration, we present the simplest non-associative geometry (based on the octonions) and evaluate its spectral action: it describes Einstein gravity coupled to a G₂ gauge theory, with 8 Dirac fermions (which transform as a singlet and a septuplet under G₂). We use this example to illustrate how non-associative geometries may be naturally linked to ordinary (associative) geometries by a certain twisting procedure. This is just the simplest example: in a forthcoming paper we show how to construct realistic models that include Higgs fields, spontaneous symmetry breaking and fermion masses.

 

[John86]

Don't miss these

http://arxiv.org/abs/1303.1537
On the theory of composition in physics
Lucien Hardy
(Submitted on 6 Mar 2013)
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such regions joined together). We propose certain fundamental axioms which, it seems, should be satisfied in any theory of composition. A key axiom is the order independence axiom which says we can describe the composition of a composite object in any order. Then we provide a notation for describing composite objects that naturally leads to these axioms being satisfied. In any given physical context we are interested in the value of certain properties for the objects (such as whether the object is possible, what probability it has, how wide it is, and so on). We associate a generalized state with an object. This can be used to calculate the value of those properties we are interested in for for this object. We then propose a certain principle, the composition principle, which says that we can determine the generalized state of a composite object from the generalized states for the components by means of a calculation having the same structure as the description of the generalized state. The composition principle provides a link between description and prediction.

http://arxiv.org/abs/1303.1538
Reconstructing quantum theory
Lucien Hardy
(Submitted on 6 Mar 2013)
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map between pure states and maximal effects such that we get unit probability. This maximal effect does not give probability equal to one for any other pure state. Information Locality: A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components. Tomographic Locality: The state of a composite system can be determined from the statistics collected by making measurements on the components. Permutability: There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. Sturdiness: Filters are non-flattening. To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.

http://arxiv.org/abs/1303.1632
Higgs potential and confinement in Yang-Mills theory on exotic R^4
Torsten Asselmeyer-Maluga, Jerzy Król
(Submitted on 7 Mar 2013)
We show that pure SU(2) Yang-Mills theory formulated on certain exotic R^4 from the radial family shows confinement. The condensation of magnetic monopoles and the qualitative form of the Higgs potential are derived from the exotic R^4, e. A relation between the Higgs potential and inflation is discussed. Then we obtain a formula for the Higgs mass and discuss a particular smoothness structure so that the Higgs mass agrees with the experimental value. The singularity in the effective dual U(1) potential has its cause by the exotic 4-geometry and agrees with the singularity in the maximal abelian gauge scenario. We will describe the Yang-Mills theory on e in some limit as the abelian-projected effective gauge theory on the standard R^4. Similar results can be derived for SU(3) Yang-Mills theory on an exotic R^4 provided dual diagonal effective gauge bosons propagate in the exotic 4-geometry.

http://arxiv.org/abs/1303.1803
Classifying gauge anomalies through SPT orders and classifying anomalies through topological orders
Xiao-Gang Wen
(Submitted on 7 Mar 2013)
In this paper, we systematically study gauge anomalies in bosonic and fermionic weak-coupling gauge theories with gauge group G (which can be continuous or discrete). We argue that, in d space-time dimensions, the gauge anomalies are described by the elements in Free[H^{d+1}(G,R/Z)]\oplus H_\pi^{d+1}(BG,R/Z). The well known Adler-Bell-Jackiw anomalies are classified by the free part of the group cohomology class H^{d+1}(G,R/Z) of the gauge group G (denoted as Free[H^{d+1}(G,\R/\Z)]). We refer other kinds of gauge anomalies beyond Adler-Bell-Jackiw anomalies as nonABJ gauge anomalies, which include Witten SU(2) global gauge anomaly. We introduce a notion of \pi-cohomology group, H_\pi^{d+1}(BG,R/Z), for the classifying space BG, which is an Abelian group and include Tor[H^{d+1}(G,R/Z)] and topological cohomology group H^{d+1}(BG,\R/\Z) as subgroups. We argue that H_\pi^{d+1}(BG,R/Z) classifies the bosonic nonABJ gauge anomalies, and partially classifies fermionic nonABJ anomalies. We also show a very close relation between gauge anomalies and symmetry-protected trivial (SPT) orders [also known as symmetry-protected topological (SPT) orders] in one-higher dimensions. Such a connection will allow us to use many well known results and well developed methods for gauge anomalies to study SPT states. In particular, the \pi-cohomology theory may give a more general description of SPT states than the group cohomology theory.

http://arxiv.org/abs/1212.4863
Boundary Degeneracy of Topological Order
Juven Wang, Xiao-Gang Wen
(Submitted on 19 Dec 2012 (v1), last revised 23 Jan 2013 (this version, v2))
We introduce the notion of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that it provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of fully gapped edge states depends on boundary gapping conditions. We develop a quantitative description of different types of boundary gapping conditions by viewing them as different ways of non-fractionalized particle condensation on the boundary. Via Chern-Simons theory, this allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which reveals more than the fusion algebra of fractionalized quasiparticles. We apply our results to Toric code and Levin-Wen string-net models. By measuring the boundary degeneracy on a cylinder, we predict Z_k gauge theory and U(1)_k x U(1)_k non-chiral fractional quantum hall state at even integer k can be experimentally distinguished. Our work refines definitions of symmetry protected topological order and intrinsic topological order.

 

[marcus]

http://arxiv.org/abs/1303.2773
BTZ Black Hole Entropy in Loop Quantum Gravity and in Spin Foam Models
J.Manuel Garcia-Islas
(Submitted on 12 Mar 2013)
We present a comparison of the calculation of BTZ black hole entropy in loop quantum gravity and in spin foam models. We see that both give the same answer.
6 pages, 3 figures

brief mention:
http://arxiv.org/abs/1303.2719
Another Survey of Foundational Attitudes Towards Quantum Mechanics
Christoph Sommer
(Submitted on 11 Mar 2013)
Although it has been almost 100 years since the beginnings of quantum mechanics, the discussions about its interpretation still do not cease. Therefore, a survey of opinions regarding this matter is of particular interest. This poll was conducted following an idea and using the methodology of Schlosshauer et al. (arXiv:1301.1069 [quant-ph]), but among a slightly different group. It is supposed to give another snapshot of attitudes towards the interpretation of quantum mechanics and keep discourse about this topic alive.
10 pages, 18 figures, 1 table

 

[tom.stoer]

Intuitive content of Loop Gravity--Rovelli's program

There is one problem with these results, namely that some people may agree that they believe in interpretation x, but that a careful analysis may also show, that they do NOT agree what this interpretation x MEANS. So without such an analysis one always misses the fact that people agreeing on Copenhagen do unfortunately not agree on the same Copenhagen :-)

 

[John86]

http://arxiv.org/abs/1303.3576
Cosmology from Group Field Theory
Steffen Gielen, Daniele Oriti, Lorenzo Sindoni
(Submitted on 14 Mar 2013)
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a non-linear and non-local extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semi-classical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.

http://arxiv.org/abs/1303.3497
The DeWitt Equation in Quantum Field Theory
Parikgarbage Dutta, Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 14 Mar 2013)
We take a new look at the DeWitt equation, a defining equation for the effective action functional in quantum field theory. We present a formal solution to this equation, and discuss the equation in various contexts, and in particular for models where it can be made completely well defined, such as the Wess-Zumino model in two dimensions.

 

[marcus]

http://arxiv.org/abs/1303.4636
Spin foams
Jonathan Engle
(Submitted on 19 Mar 2013)
The spin foam framework provides a way to define the dynamics of canonical loop quantum gravity in a spacetime covariant way, by using a path integral over histories of quantum states which can be interpreted as 'quantum space-times'. This chapter provides a basic introduction to spin foams aimed principally at beginning graduate students and, where possible, at broader audiences.
32 pages, 14 figures, 2 tables, to appear as a chapter of "The Springer Handbook of Spacetime," edited by A. Ashtekar and V. Petkov (Springer-Verlag 2013)

http://arxiv.org/abs/1303.4294
Constraint analysis for variational discrete systems
Bianca Dittrich, Philipp A Hoehn
(Submitted on 18 Mar 2013)
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves and naturally incorporates both constant and evolving phase spaces, the latter of which is necessary for a time varying discretization. The different roles of constraints in the discrete and the conditions under which they are first or second class and/or symmetry generators are clarified. The (non-) preservation of constraints and the symplectic structure is discussed; on evolving phase spaces the number of constraints at a fixed time step depends on the initial and final time step of evolution. Moreover, the definition of observables and a reduced phase space is provided; again, on evolving phase spaces the notion of an observable as a propagating degree of freedom requires specification of an initial and final step and crucially depends on this choice, in contrast to the continuum. However, upon restriction to translation invariant systems, one regains the usual time step independence of canonical concepts. These results are applicable, e.g., to discrete mechanics, lattice field theory, quantum gravity models and numerical analysis.
48 pages, many figures

brief mention:
http://arxiv.org/abs/1303.3935
Quantum mechanics from invariance laws
Florin Moldoveanu
(Submitted on 16 Mar 2013)

 

[marcus]

http://arxiv.org/abs/1303.4752
Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
Norbert Bodendorfer, Yasha Neiman
(Submitted on 19 Mar 2013)
It was recently noted that the on-shell Einstein-Hilbert action with York-Gibbons-Hawking boundary term has an imaginary part, proportional to the area of the codimension-2 surfaces on which the boundary normal becomes null. We extend this result to first-order formulations of gravity, by generalizing a previously proposed boundary term to closed boundaries. As a side effect, we settle the issue of the Holst modification vs. the Nieh-Yan density by demanding a well-defined variational principle. We then set out to find the imaginary action in the large-spin 4-simplex limit of the Lorentzian EPRL/FK spinfoam. It turns out that the spinfoam's effective action indeed has the correct imaginary part, but only if the Barbero-Immirzi parameter is set to +/- i after the quantum calculation. An interpretation and a connection to other recent results is discussed. In particular, we propose that the large-spin limit of loop quantum gravity can be viewed as a high-energy 'transplanckian' regime.
22 pages, 5 figures

http://arxiv.org/abs/1303.4989
Loop Quantum Gravity and the The Planck Regime of Cosmology
Abhay Ashtekar
(Submitted on 20 Mar 2013)
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
23 pages, 4 figures. Plenary talk at the Conference: Relativity and Gravitation: 100 Years after Einstein in Prague. To appear in the Proceedings to be published by Edition Open Access. Summarizes results that appeared in journal articles [2-13]

http://arxiv.org/abs/1303.4829
Thermodynamics of Quantum Isolated Horizon in Canonical Ensemble
Abhishek Majhi
(Submitted on 20 Mar 2013)
The derivation of the microcanonical entropy of a Quantum Isolated Horizon(QIH), directly from the associated quantum Chern-Simons(CS) theory, in terms of the two parameters characterizing the QIH, namely the level of the associated CS theory (k) and the total number of punctures of the QIH (N), is reviewed. With a view to extend the thermodynamic analysis to the Canonical Ensemble a model energy spectrum for the QIH is proposed from a complete quantum view point using the available elements of Loop Quantum Gravity (LQG). The study of thermodynamics of QIH in the Canonical Ensemble reveals that, in the LQG framework, for a quantum spacetime admitting a thermodynamically stable QIH as its internal boundary, must have a specific bound on the Barbero-Immirzi(BI) parameter if the entropy of the QIH obeys the Bekenstein-Hawking Area Law. To mention, the complete analysis, especially the used energy spectrum of the QIH, has been performed from a complete quantum viewpoint.
23 pages

http://arxiv.org/abs/1303.4832
A Model Hamiltonian for Quantum Isolated Horizon
Abhishek Majhi
(Submitted on 20 Mar 2013)
With a view to clarify some apparent inconsistencies in the classical and quantum theories of Isolated Horizon and motivated by the structure of the area operator in loop quantum gravity, a model Hamiltonian operator for the quantum Isolated Horizon is proposed. Known results of Isolated Horizon thermodynamics are used as inputs to fix the model. The proposal of the model is based on the facts that the Hamiltonian operator and the area operator associated with the quantum Isolated Horizon should have simultaneous eigenstates and in the correspondence limit one must obtain that the area of a classical Isolated Horizon is constant.
9 pages

 

[marcus]

http://arxiv.org/abs/1303.5612
A Gravitational Entropy Proposal
Timothy Clifton, George F R Ellis, Reza Tavakol
(Submitted on 22 Mar 2013)
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein-Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein's field equations. It is also in keeping with Penrose's Weyl curvature hypothesis.
17 pages

 

[marcus]

http://arxiv.org/abs/1303.6157
Loop quantum dynamics of the gravitational collapse
Yaser Tavakoli, Joao Marto, Andrea Dapor
(Submitted on 25 Mar 2013)
We consider a quantum description for a spherically symmetric gravitational collapse of a massless scalar field. The effective scenario from loop quantum gravity is applied to a homogeneous interior spacetime. Classical singularity that arises at the final stage of our collapsing system, is resolved and replaced by a quantum bounce. Our main purpose is to investigate the evolution of trapped surfaces during the collapse in semiclassical regime. We show that, in this regime, there exists a threshold scale bellow which no horizon can form as collapse evolves towards the bounce. By employing the matching conditions at the boundary shell, quantum effects are carried out to the exterior region, leading to an improved Vaidya geometry. In addition, the effective mass loss emerging in this model predicts an outward energy flux from the interior quantum geometry regime.
11 pages, 5 figures

 

[marcus]

http://arxiv.org/abs/1303.6772
Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau
(Submitted on 27 Mar 2013)
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.
47 pages, 8 figures, 2 tables

brief mention, not QG but possibly of interest:
http://arxiv.org/abs/1303.6912
News on Right Handed Neutrinos
Marco Drewes
(Submitted on 27 Mar 2013)
Neutrinos are the only particles in the Standard Model of particle physics that have only been observed with left handed chirality to date. If right handed neutrinos exist, they could be responsible for several phenomena that have no explanation within the Standard Model, including neutrino oscillations, the baryon asymmetry of the universe, dark matter and dark radiation. After a pedagogical introduction, we review recent progress in the phenomenology of right handed neutrinos. We in particular discuss the mass ranges suggested by hints for neutrino oscillation anomalies and dark radiation (eV), sterile neutrino dark matter scenarios (keV) and experimentally testable theories of baryogenesis (GeV to TeV). We summarize constraints from theoretical considerations, laboratory experiments, astrophysics and cosmology for each of these.
Comments: 44 pages, 14 figures

 

[marcus]

http://arxiv.org/abs/1303.7139
Symmetry and Evolution in Quantum Gravity
Sean Gryb, Karim Thebault
(Submitted on 28 Mar 2013)
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory makes predictions that are distinct from Wheeler-DeWitt cosmology. Furthermore, the local symmetry principle - and corresponding observables - of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.
36 preprint pages. 1 table

http://arxiv.org/abs/1303.7216
Relative Locality in Curved Space-time
Jerzy Kowalski-Glikman, Giacomo Rosati
(Submitted on 28 Mar 2013)
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.

 

[marcus]

brief mention
(relevant to QG, see conclusions):
http://arxiv.org/abs/1303.7371
Spheres are rare
Vincent Rivasseau
(Submitted on 29 Mar 2013)
We prove that triangulations of homology spheres in any dimension grow much slower than general triangulations. Our bound states in particular that the number of triangulations of homology spheres in 3 dimensions grows at most like the power 1/3 of the number of general triangulations.
14 pages, 1 figure

 

[marcus]

http://arxiv.org/abs/1304.0209
Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity
Yu Han, Yongge Ma, Xiangdong Zhang
(Submitted on 31 Mar 2013)
The scalar-tensor theories of gravity in spacetime dimensions D+1>2 are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter ω. The Hamiltonian structure in both sectors are similar to the corresponding structure of 4-dimensional cases. It turns out that there is a symplectic reduction from the canonical structure of so(D+1) Yang-Mills theories coupled to the scalar field to the canonical structure of the geometrical scalar-tensor theories. Therefore the non-perturbative loop quantum gravity techniques can also be applied to the scalar-tensor theories in D+1 dimensions based on their connection-dynamical formalism.
13 pages