Framework Of Loop Quantum Gravity Research Articles

Realization of Dirac quantization in loop quantum gravity

The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to two versions of well-defined operators in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian can become some symmetric operators. By the deparametrized form, a general expression of the solutions to either of the quantum scalar constraints is obtained, and the observables on the space of solutions can be constructed. Thus, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system.

Thermodynamics of isolated horizons in loop quantum gravity

The statistical mechanical calculation of the thermodynamical properties of nonrotating isolated horizons are studied in the loop quantum gravity framework. By employing the Hawking temperature and horizon mass of isolated horizons as physical inputs, the microcanonical ensemble associated with the system are well established. As a result, the black hole entropy and other thermodynamical quantities can be computed and are consistent with well-known Hawking's semiclassical analysis. Moreover, the value of the Immirzi parameter of loop quantum gravity for the higher-dimensional case and four-dimensional U(1) case are also obtained.

Intertwiner entanglement excitation and holonomy operator

In the loop quantum gravity framework, spin network states carry entanglement between quantum excitations of the geometry at different space points. This intertwiner entanglement is gauge-invariant and comes from quantum superposition of spins and intertwiners. Bipartite entanglement can be interpreted as a witness of distance, while multipartite entanglement reflects the curvature of the quantum geometry. The present work investigates how the bipartite and multipartite intertwiner entanglement changes under the action of the holonomy operator, which is the basic building block of loop quantum gravity’s dynamics. We reveal the relation between entanglement excitation and the dispersion of the holonomy operator. This leads to a new interesting connection between bulk geometry and boundary observables via the dynamics of entanglement.

Loop representation and r -Fock measures for SU(N) gauge theories

In this article we continue the work on translating elements of the perturbative quantum field theory defined on Minkowski spacetime into the background independent framework of Loop Quantum Gravity. We present the construction of r-Fock measures for $SU(N)$ gauge theories and provide a relation between these new r-Fock measures and the difeomorphism invariant measure used in loop quantum gravity.

(4 + 4)-Dimensional Space-Time as a Dual Scenario for Quantum Gravity and Dark Matter

In this work, we make a number of proposals to explain how a world of (4 + 4)-dimensions can be useful for a better understanding of both dark matter and quantum gravity. The key idea is to look for some advantage of considering self-dual invariants in (4 + 4)-dimensions rather than in a separate context of (1 + 3)-dimensions or (3 + 1)-dimensions. In fact, we show that by considering the duality concept in (4 + 4)-dimensions we may provide an alternative meaning of a framework for loop quantum gravity. Moreover, considering the Dirac equation in (4 + 4)-dimensions for a particle without electric charge and mass, we show that when it is projected into the (1 + 3) and (3 + 1)-worlds may describe a system with electric charge and mass. We also discuss the relation between the three physical scenarios; (4 + 4)-world, black-holes and dark matter.

Extended geometry of Gambini-Olmedo-Pullin polymer black hole and its quasinormal spectrum

In this paper we systematically study a model of spherically symmetric polymer black holes recently proposed by Gambini, Olmedo, and Pullin (GOP). Within the framework of loop quantum gravity, the quantum parameters in the GOP model depend on the minimal area gap and the size of the discretization of the physical states. In this model, a spacelike transition surface takes place of the classical singularity. By means of coordinate transformations, we first extend the metric to the white hole region, and find that the geometric structure of the quantum black hole is similar to the wormhole structure, and the radius of the most quantum region is equal to the wormhole radius. In addition, we show that the energy conditions are violated not only at throat, but also at horizons and the spatial infinities. In order to show how the quantum effects affect the spacetimes, we calculate the Ricci and Kretschmann scalars at different places. It turns out that, as expected, the most quantum region is at the throat. Finally, we consider the quasinormal modes (QNMs) of massless scalar field perturbations, electromagnetic field perturbations, and axial gravitational perturbations. QNMs in the Eikonal limits are also considered. As anticipated, the spectrum of QNMs deviates from that of the classical case due to quantum effects. Interestingly, our results show that the quasinormal frequencies of the perturbations share the same qualitative tendency while setting quantum parameters with various values in this effective model, even if the potential deviations are different with different spins.

Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for mathcal{N} = 1 and mathcal{N} = 2 pure AdS supergravity in D = 4 for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the mathcal{N} = 2 case, it follows that this amounts to the introduction of a θ-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the θ-ambiguity of gauge theory.We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with OSp( mathcal{N} |2) gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D’Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravity.

Kinematics of arbitrary spin matter fields in loop quantum gravity

Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity. There is a general understanding of how to formulate scalar fields, spin $\frac{1}{2}$ fields, and gauge fields in the framework of loop quantum gravity. The goal of the present work is to investigate kinematical aspects of this coupling. We will study implications of the Gau\ss{} and diffeomorphism constraints for the quantum theory: We define and study a less ambiguous variant of the Baez-Krasnov path observables, and we investigate symmetry properties of spin network states imposed by diffeomorphism group averaging. We will do this in a setting which allows for matter excitations of spin $\frac{1}{2}$ and higher. In the case of spin $\frac{1}{2}$, we will also discuss extensions of it by introducing an electromagnetic field and antiparticles. We finally discuss how far the picture with matter excitations of higher spin can be obtained from classical actions for higher spin fields.

N=1Supergravity with loop quantum gravity methods and quantization of the SUSY constraint

In this paper, the classical and quantum theory of $\mathcal{N}=1$ supergravity in four spacetime dimensions will be studied in the framework of loop quantum gravity. We discuss the canonical analysis of the supergravity Holst action as first introduced by Tsuda. In this way, we also derive a compact expression of the supersymmetry constraint, which plays a crucial role in canonical supergravity theories, akin to the role of the Hamiltonian constraint in non-supersymmetric generally covariant theories. The resulting theory is then quantized using loop quantum gravity methods. In particular, we propose and discuss a quantization of the supersymmetry constraint and derive explicit expressions of the action of the resulting operator. This is important as it is the first step on the way of analyzing the Dirac algebra generated by supersymmetry and Hamiltonian constraint in the quantum theory and for finding physical states. We also discuss some qualitative properties of such solutions of the SUSY constraint.

Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections

This article concerns the problems regarding different lattice regularization techniques for the matter fields of Hamiltonian constraints defined in the framework of loop quantum gravity. The analysis is formulated in the phase space-reduced cosmological model of the hypothetical theory of canonical quantum general relativity. This article explains why a different than links-related lattice smearing of fields leads to a local violation of general covariance. This happens by assuming, for instance, the nodes-related smearing. Therefore, this problem occurs in the case of any polymerlike scalar field quantization method by breaking the background independence of the semiclassical predictions. In consequence, the diffeomorphism symmetry that depends on a links distribution is broken locally at the level of generally relativistic corrections. Moreover, by using the phase space-reduced gauge fixing technique to analyze this issue, the results are general and they concern any coupling with the links-regularized gravitational degrees of freedom in loop quantum gravity. Therefore, they lead to the following no-go conclusion. Any lattice smearing of matter, not defined by using the geometrical distribution specified by the links-fluxes duality, violates the general principle of relativity.

Effective loop quantum gravity framework for vacuum spherically symmetric spacetimes

We develop an effective framework for the $\bar\mu$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory, and then expressing the remaining components of the Ashtekar-Barbero connection in the Hamiltonian constraint in terms of holonomies of physical length $\ell_{\rm Pl}$. The stationary solutions to the effective Hamiltonian constraint can be found exactly, and we give the explicit form of the effective metric in Painlev\'e-Gullstrand coordinates. This solution has the correct classical limit, the quantum gravity corrections decay rapidly at large distances, and curvature scalars are bounded by the Planck scale, independently of the black hole mass $M$. In addition, the solution is valid for radii $x \ge x_{\rm min} \sim (\ell_{\rm Pl}^2 M)^{1/3}$ indicating the need for a matter field, with an energy density bounded by the Planck scale, to provide a source for the curvature in the space-time. Finally, for $M \gg m_{\rm Pl}$, the space-time has an outer and also an inner horizon, within which the expansion for outgoing radial null geodesics becomes positive again. On the other hand, for sufficiently small $M \sim m_{\rm Pl}$, there are no horizons at all in the effective metric.

A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes

We investigate the interior structure, perturbations, and the associated quasinormal modes of a quantum black hole model recently proposed by Bodendorfer, Mele, and Münch (BMM). Within the framework of loop quantum gravity, the quantum parameters in the BMM model are introduced through polymerization, consequently replacing the Schwarzschild singularity with a spacelike transition surface. By treating the quantum geometry corrections as an `effective' matter contribution, we first prove the violation of energy conditions (in particular the null energy condition) near the transition surface and then investigate the required junction conditions on it. In addition, we study the quasinormal modes of massless scalar field perturbations, electromagnetic perturbations, and axial gravitational perturbations in this effective model. As expected, the quasinormal spectra deviate from their classical counterparts in the presence of quantum corrections. Interestingly, we find that the quasinormal frequencies of perturbations with different spins share the same qualitative tendency with respect to the change of the quantum parameters in this model.

Reduced loop quantization with four Klein–Gordon scalar fields as reference matter

We perform a reduced phase space quantization of gravity using four Klein–Gordon scalar fields as reference matter as an alternative to the Brown–Kuchar dust model in Giesel and Thiemann (2010 Class. Quantum Grav. 27 175009), where dust scalar fields are used. We compare our results to an earlier model by Domagala et al (2010 Phys. Rev. D 82 104038) where only one Klein–Gordon scalar field is considered as reference matter for the Hamiltonian constraint but the spatial diffeomorphism constraints are quantized using Dirac quantization. As a result we find that the choice of four conventional Klein–Gordon scalar fields as reference matter leads to a reduced dynamical model that cannot be quantized using loop quantum gravity techniques. However, we further discuss a slight generalization of the action for the four Klein–Gordon scalar fields and show that this leads to a model which can be quantized in the framework of loop quantum gravity. By comparison of the physical Hamiltonian operators obtained from the model by Domagala et al (2010 Phys. Rev. D 82 104038) and the one introduced in this work we are able to make a first step towards comparing Dirac and reduced phase space quantization in the context of the spatial diffeomorphism constraints.

Phenomenology of quantum reduced loop gravity in the isotropic cosmological sector

Quantum reduced loop gravity is designed to consistently study symmetry reduced systems within the loop quantum gravity framework. In particular, it bridges the gap between the effective cosmological models of loop quantum cosmology and the full theory, addressing the dynamics before the minisuperspace reduction. This mostly preserves the graph structure and SU(2) quantum numbers. In this article, we study the phenomenological consequences of the isotropic sector of the theory, the so-called emergent bouncing universe model. In particular, the parameter space is scanned and we show that the number of inflationary e-folds is almost always higher than the observational lower-bound. We also compute the primordial tensor power spectrum and study its sensitivity upon the fundamental parameters used in the model.

From coarse-graining to holography in loop quantum gravity

We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we integrating out physical degrees of freedom or gauge degrees of freedom? Since the distinction between physical and gauge degrees of freedom is encoded in the dynamics of the theory, this highlights the crucial role of the dynamics in understanding the coarse-graining. Focusing on how bulk spin network states for bounded regions of space are projected onto boundary states, we show that all possible boundary states can be recovered from bulk spin networks with a single vertex in the bulk and a single internal loop attached to it. This partial reconstruction of the bulk from the boundary leads us to the idea of realizing the Hamiltonian constraints at the quantum level as a gauge equivalence reducing arbitrary spin network states to one-loop bulk states. This proposal of “dynamics through coarse-graining” would lead to a one-to-one map between equivalence classes of physical states under gauge transformations and boundary states, thus defining holographic dynamics for loop quantum gravity.

Discretization of 3d gravity in different polarizations

We study the discretization of 3d gravity with $\Lambda=0$ following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical non-trivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

Gravity as an SU(1, 1) gauge theory in four dimensions

We start with the Hamiltonian formulation of the first order action of pure gravity with a full internal gauge symmetry. We make a partial gauge-fixing which reduces to its sub-algebra . This case corresponds to a splitting of the space-time where inherits an arbitrary Lorentzian metric of signature (−, +, +). Then, we find a parametrization of the phase space in terms of an commutative connection and its associated conjugate electric field. Following the techniques of loop quantum gravity, we start the quantization of the theory and we consider the kinematical Hilbert space on a given fixed graph whose edges are colored with unitary representations of . We compute the spectrum of area operators acting on the kinematical Hilbert space: we show that space-like areas have discrete spectra, in agreement with usual loop quantum gravity, whereas time-like areas have continuous spectra. We conclude on the possibility to make use of this formulation of gravity to construct a holographic description of black holes in the framework of loop quantum gravity.

A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity

We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.

Proof of Bekenstein–Mukhanov ansatz in loop quantum gravity

In this paper, a simple proof of Bekenstein–Mukhanov (BM) ansatz is given within the loop quantum gravity (LQG) framework. The macroscopic area of an equilibrium black hole horizon indeed manifests a linear quantization. The quantum number responsible for this discreteness of the macroscopic area has a physical meaning in the LQG framework, unlike the ad hoc one that remained unexplained in BM ansatz.

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).