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Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase—a topic of recent focus in spin-foams—but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis. The covariant formulation of gravity from which spin-foams are derived is the Plebanski–Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued 2-form, called the Plebanski 2-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski 2-form alone. The spin-foam sum is therefore a discretized version of a Plebanski–Holst path integral in which only the Plebanski 2-form appears, and in which the connection degrees of freedom have been integrated out. We call this a purely geometric Plebanski–Holst path integral. In prior work in which one of the authors was involved, the measure factor for the Plebanski–Holst path integral with both connection and 2-form variables was calculated. Before one discretizes this measure and incorporates it into a spin-foam sum, however, one must integrate out the connection in order to obtain the purely geometric version of the path integral. To calculate this purely geometric path integral is the principal task of the present paper, and it is done in two independent ways. Background independence of the resulting path integral is discussed in the final section, and gauge-fixing is discussed in appendix B. [ABSTRACT FROM AUTHOR]

New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields Bμν and C, which was introduced in Fujisawa and Nakayama (2014 Class. Quantum Grav.31 015003), is formulated. By using a local symmetry, two of the components of Bμν are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, Bϕρ, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields Aμ, . In this model, solutions to the classical equations of motion for Aμ and are non-flat due to the interactions with matter fields. The solutions for the gauge fields can, however, be split into two parts, flat gauge fields , , and those terms that depend on the matter fields. The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds and , which are exactly the same as those in linearized 3d Vasiliev gravity. The two- and three-point correlation functions of the single-trace operators and the higher-spin currents in the boundary CFT are computed by using an on-shell action tr (Bϕρ C). This term does not depend on coordinates due to the matter equations of motion, and it is not necessary to take the near-boundary limit ρ → ∞. Analysis is presented for SL(3,R) × SL(3,R) as well as higher-spin gravity. In the latter model, scalar operators with scaling dimensions Δ+ = 3/2 and Δ− = 1/2 appear in a single quantization. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a Chern–Simons theory on the boundary in the four-dimensional case, to non-distorted isolated horizons in 2(n + 1)-dimensional spacetimes. The key idea is to generalize the four-dimensional isolated horizon boundary condition by using the Euler topological density E(2n) of a spatial slice of the black hole horizon as a measure of distortion. The resulting symplectic structure on the horizon coincides with the one of higher-dimensional SO(2(n + 1))-Chern–Simons theory in terms of a Peldan-type hybrid connection Γ0 and resembles closely the usual treatment in (3 + 1) dimensions. We comment briefly on a possible quantization of the horizon theory. Here, some subtleties arise since higher-dimensional non-Abelian Chern–Simons theory has local degrees of freedom. However, when replacing the natural generalization to higher dimensions of the usual boundary condition by an equally natural stronger one, it is conceivable that the problems originating from the local degrees of freedom are avoided, thus possibly resulting in a finite entropy. [ABSTRACT FROM AUTHOR]

Quantum gravity is sometimes considered as a kind of metaphysical speculation. In this review, we show that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an invaluable laboratory to probe ‘Planck scale physics’. Focusing on loop quantum gravity as one of the best candidate for a non-perturbative and background-independent quantization of gravity, we detail some expected features. [ABSTRACT FROM AUTHOR]

We consider the k = 1 Friedman–Lemaitre–Robertson–Walker model within loop quantum cosmology, from the perspective of the two available quantization prescriptions. We focus our attention on the existence of the so-called ‘inverse corrections’ in the quantization process. We derive the corresponding quantum constraint operators, and study in detail the issue of the self-adjointness of the quantum Hamiltonian constraint for two different quantizations based on open holonomies. Furthermore, we analyse in detail the resulting effective theories, paying special attention to issues such as the boundedness of different scalar observables such as energy density and expansion. We show that the inclusion of the inverse corrections solves one of the main undesirable features of the previous formalism, namely the unboundedness of the energy density and expansion near the bounce on the full (effective) phase space. We briefly comment on possible consequences of this new feature. Communicated by P Singh [ABSTRACT FROM AUTHOR]

Quantization of relativistic point particles coupled to three-dimensional Einstein gravity naturally leads to field theories living on the Lorentz group in their momentum representation. The Lie group structure of momentum space can be traced back to the classical phase space of the particles coupled to topological gravity. In this work we show how the non-trivial structure of momentum space leads to an unusual description of Fock space. The latter is reflected in a deformed algebra of creation and annihilation operators which reduces to the ordinary algebra when momentum space ‘flattens’ to Minkowski space in the limit in which the three-dimensional Newton’s constant vanishes. The construction is covariant under the action of relativistic symmetries acting on the Lorentz group-momentum space. This shows how it is possible to build a Fock space on a group manifold momentum space in a way consistent with the underlying (deformed) relativistic symmetries. [ABSTRACT FROM AUTHOR]

We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann–Lemaître–Robertson–Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar–Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann–Lemaître–Robertson–Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role. [ABSTRACT FROM AUTHOR]

In the previous paper, we examined the third quantization of the f(R)-type gravity and studied the Heisenberg uncertainty relation of the universe in the example of f(R) = R2. In this work, the Heisenberg uncertainty relation of the universe is investigated in the general f(R)-type gravity where tachyonic states are avoided. It is shown that, at late times namely the scale factor of the universe is large, the spacetime becomes classical, and, at early times namely the scale factor of the universe is small, the quantum effects dominate. [ABSTRACT FROM AUTHOR]

A generalization of the representation, underlying the discrete spatial geometry of loop quantum gravity, to accomodate states labelled by smooth spatial geometries, was discovered by Koslowski and further studied by Sahlmann. We show how to construct the diffeomorphism constraint operator in this Koslowski-Sahlmann (KS) representation from suitable connection and triad dependent operators. We show that the KS representation supports the action of hitherto unnoticed 'background exponential' operators which, in contrast to the holonomy-flux operators, change the smooth spatial geometry label of the states. These operators are shown to be quantizations of certain connection dependent functions and play a key role in the construction of the diffeomorphism constraint operator. [ABSTRACT FROM AUTHOR]

We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillatormay be relevant for the discussion of the polymer quantization of the scalar field and may have interesting consequences for the statistical mechanics of these models. [ABSTRACT FROM AUTHOR]

Polymer quantization is a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer Hilbert space we show that they converge in the limit of vanishing polymer scale. We derive a general bound that relates entropies of physically equivalent states in unitarily inequivalent representations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational details and extend the results to standard model matter, a cosmological constant, and non-compact spatial slices. On the other hand, we provide a discussion on the role of observables, focused on the situation of a symmetry exchange, which is key to our derivation. Furthermore, we comment on the relation of our model to reduced phase space quantizations based on deparametrization. [ABSTRACT FROM AUTHOR]

We consider matter fields conformally coupled to a background metric and dilaton and describe in detail a quantization procedure and related renormalization group flow that preserve Weyl invariance. Even though the resulting effective action is Weyl-invariant, the trace anomaly is still present, with all its physical consequences. We discuss first the case of free matter and then extend the result to interacting matter. We also consider the case when the metric and dilaton are dynamical and gravitons enter the loops. [ABSTRACT FROM AUTHOR]

The one-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them loop quantum gravity and spin foams. It facilitates the loop quantization programme and subsequently the Barbero-Immirzi parameter (? ) arises in both the spectra of geometrical operators and in the dynamics provided by spin foams. However, the debate continues as to whether quantum physics should be Barbero-Immirzi parameter dependent. Starting from a discrete SO(4)-BF theory phase space, we find two possible reductions with respect to a discrete form of the simplicity constraints. The first reduces to a phase space with ? -dependent symplectic structure and more generally in agreement with the phase space underlying loop quantum gravity restricted to a single graph-- a.k.a. twisted geometries. The second, fuller reduction leads to a ? -independent symplectic structure on the phase space of piecewise-flat-linear geometries-- a.k.a Regge geometries. Thus, the ? -dependence of physical predictions is related to the choice of phase space underlying the quantization. [ABSTRACT FROM AUTHOR]

We present a model of the gravitational field based on two symmetric tensors. Gravity is affected by the new field, but if Tμv = 0, the predictions of the model coincide exactly with general relativity, so all classical tests are satisfied. We find that massive particles do not follow a geodesic, while massless particles trajectories are null geodesics of an effective metric. We study the cosmological case, where we obtain an accelerated expansion of the Universe without dark energy. [ABSTRACT FROM AUTHOR]

We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum. [ABSTRACT FROM AUTHOR]

We consider the quantization of scalar fields on aLifshitz background, exploring the possibility of alternative boundary conditions, allowing the slow falloff mode to fluctuate. We show that the scalar field with alternative boundary conditions is normalizable for a larger range of masses than in the AdS case. However, we then find a new instability for alternative boundary conditions, implying that the range of masses where alternative boundary conditions define a well-behaved dual theory is m² BF < m² < m² BF + 1, analogously to the AdS case. The instability is of a novel type, with modes of arbitrarily large momentum which grow exponentially in time; it is therefore essentially a UV effect, and implies that the dual field theory is simply not defined where it appears. We discuss the interpretation in the dual field theory, and give a proposed lower bound on the dimension of scalar operators. [ABSTRACT FROM AUTHOR]

We consider spherically symmetric black holes in generic Lovelock gravity. Using geometrodynamical variables we do a complete Hamiltonian analysis, including derivation of the super-Hamiltonian and super-momentum constraints and verification of suitable boundary conditions for asymptotically flat black holes. Our analysis leads to a remarkably simple fully reduced Hamiltonian for the vacuum gravitational sector that provides the starting point for the quantization of Lovelock block holes. Finally,we derive the completely reduced equations of motion for the collapse of a spherically symmetric, charged selfgravitating complex scalar field in generalized flat slice (Painlevé-Gullstrand) coordinates. [ABSTRACT FROM AUTHOR]

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for different choices of combinatorialweights. Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation. As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs. [ABSTRACT FROM AUTHOR]

We offer a new, physically transparent argument for the existence of the critical, universal maximum matter density in loop quantum cosmology for the case of a flat Friedmann-Lemâıtre-Robertson-Walker cosmology with scalar matter. The argument is based on the existence of a sharp exponential ultraviolet cutoff in momentum space on the eigenfunctions of the quantum cosmological dynamical evolution operator (the gravitational part of the Hamiltonian constraint), attributable to the fundamental discreteness of spatial volume in loop quantum cosmology. The existence of the cutoff is proved directly from recently found exact solutions for the eigenfunctions for this model. As a consequence, the operators corresponding to the momentum of the scalar field and the spatial volume approximately commute. The ultraviolet cutoff then implies that the scalar momentum, though not a bounded operator, is in effect bounded on subspaces of constant volume, leading to the upper bound on the expectation value of the matter density. The maximum matter density is universal (i.e. independent of the quantum state) because of the linear scaling of the cutoff with volume. These heuristic arguments are supplemented by a new proof in the volume representation of the existence of the maximum matter density. The techniques employed to demonstrate the existence of the cutoff also allow us to extract the large-volume limit of the exact eigenfunctions, confirming earlier numerical and analytical work showing that the eigenfunctions approach superpositions of the eigenfunctions of the Wheeler-DeWitt quantization of the same model. We argue that generic (not just semiclassical) quantum states approach symmetric superpositions of expanding and contracting universes. [ABSTRACT FROM AUTHOR]

We quantize the particle dynamics in AdSN+1× SM spacetime in static gauge, which leads to the coordinate representation with wavefunctions depending only on spatial coordinates. The energy square operator is quadratic in canonical momenta and contains a scalar curvature term. We analyze the selfadjointness of this operator and calculate its spectrum. We then construct unitary representations of the isometry group SO(2,N)× SO(M + 1) and calculate the quantum relation between the Casimir numbers. [ABSTRACT FROM AUTHOR]

A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations provided insights into the resolution of classical singularities, resulting in the key prediction of the bounce at the Planck scale in different models, and the numerical methods used to analyze the properties of the quantum difference operator and the von Neumann stability issues. Using the quantization of a massless scalar field in an isotropic spacetime as a template, an attempt is made to highlight the complementarity of different methods to gain understanding of the new physics emerging from the quantum theory. Open directions which need to be explored with more refined numerical methods are discussed. [ABSTRACT FROM AUTHOR]

We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in d ﹥ 2 dimensions. We show that this is inequivalent to what is obtained from applying the Faddeev-Popov (FP) procedure directly. Due to the presence of tertiary first class constraints, the measure of the path integral is found to have a substantially different structure from what arises in the FP approach. In addition, the presence of second class constraints leads to non-trivial ghosts, which cannot be absorbed into the normalization of the path integral. The measure of the path integral lacks manifest covariance. [ABSTRACT FROM AUTHOR]

We examine the third quantization of f (R)-type gravity, based on its effective Lagrangian in the case of a flat Friedmann-Lemaitre-Robertson-Walker metric. Starting from the effective Lagrangian, we make a suitable change of variable and the second quantization, and we obtain the Wheeler-DeWitt equation. The third quantization of this theory has been considered. The uncertainty relation of the universe has been investigated in the example of f (R)-type gravity, where f (R) = R2. It has been shown that, at late times namely the scale factor of the universe is large, the spacetime does not contradict to become classical, and, at early times namely the scale factor of the universe is small, the quantum effects dominate. [ABSTRACT FROM AUTHOR]

We show that general relativity can be formulated as a constrained topological theory for flat 2-connections associated with the Poincar'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge lengths of the spacetimemanifold triangulation arise as the basic variables in the path-integral quantization, while the state-sum amplitude is an evaluation of a colored 3-complex, in agreement with the category theory results. A 3-complex amplitude for Euclidean quantum gravity is proposed. [ABSTRACT FROM AUTHOR]

D = 2 + 1 gravity with a cosmological constant has been shown by Bonzom and Livine to present a Barbero-Immirzi-like ambiguity depending on a parameter γ . We make use of this fact to show that, for &Lgr; > 0, the Lorentzian theory can be partially gauge fixed and reduced to an SU(2) Chern- Simons theory. We then review the already known quantization of the latter in the framework of loop quantization for the case of space being topologically a cylinder. We finally construct, in the same setting, a quantum observable which, although non-trivial at the quantum level, corresponds to a null classical quantity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the quantization of the 2D BF model coupled to topological matter. Guided by the rigid supersymmetry, this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of loop quantum gravity methods. [ABSTRACT FROM AUTHOR]

We show that the degenerate sector of Spin(4) Plebanski formulation of fourdimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2) Crane-Yetter model and allows to test various approaches of imposing the simplicity constraints. Our analysis strongly suggests that restricting representations and intertwiners in the state sum for Spin(4) BF theory is not sufficient to get the correct vertex amplitude. Instead, for a general theory of Plebanski type, we propose a quantization procedure which is by construction equivalent to the canonical path integral quantization and, being applied to our model, reproduces the SU(2) Crane-Yetter state sum. A characteristic feature of this procedure is the use of secondary second class constraints on an equal footing with the primary simplicity constraints, which leads to a new formula for the vertex amplitude. [ABSTRACT FROM AUTHOR]

We introduce a three-dimensional Plebanski action for the gauge group SO(4). In this model, the B field satisfies quadratic simplicity constraints similar to that of the four-dimensional Plebanski theory, but with the difference that the B field is now a 1-form. We exhibit a natural notion of 'simple 1-form', and identify a gravitational sector, a topological sector and a degenerate sector in the space of solutions to the simplicity constraints. Classically, in the gravitational sector, the action is shown to be equivalent to that of three-dimensional firstorder Riemannian gravity. This enables us to perform the complete spin foam quantization of the theory once the simplicity constraints are solved at the classical level, and to compare this result with the various models that have been proposed for the implementation of the constraints after quantization. In particular, we impose the simplicity constraints following the prescriptions of the so-called BC and EPRL models. We observe that the BC prescription cannot lead to the proper vertex amplitude. The EPRL prescription allows us to recover the expected result when, in this three-dimensional model, it is supplemented with additional secondary second class constraints. [ABSTRACT FROM AUTHOR]

We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of Dirac observables and an internal clock. We obtain the physical Hilbert space, which is the carrier space of the self-adjoint representation of the Dirac observables. Then, we discuss the problem of time. We demonstrate that the inclusion of evolution in a gravitational system, at classical level as well as at quantum level, leads respectively to canonically and unitarily inequivalent theories. The example of Hubble operator in two different clock variables and with two distinct spectra is given. [ABSTRACT FROM AUTHOR]

We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedmann-Robertson-Walker model coupled to a massless scalar field. We identify the physical quantum Hamiltonian that is positive-definite and generates globally a unitary evolution of the considered quantum system. We examine the properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of evolved observables is studied for the Gaussian state. Calculated relative fluctuations enable an examination of the semi-classicality conditions and possible occurrence of the cosmic forgetfulness. Preliminary estimations based on the cosmological data suggest that there was no cosmic amnesia. Presented results are analytical, and numerical computations are only used for the visualization purposes. Our method may be generalized to sophisticated cosmological models including the Bianchi-type universes. [ABSTRACT FROM AUTHOR]

The polarized Gowdy model in terms of Ashtekar-Barbero variables is reduced with an additional constraint derived from the Killing equations for plane gravitational waves with parallel rays. The new constraint is formulated in a diffeomorphism invariant manner and, when it is included in the model, the resulting constraint algebra is first class, in contrast to the prior work done in special coordinates. Using an earlierwork by Banerjee and Date, the constraints are expressed in terms of classical quantities that have an operator equivalent in loop quantum gravity, making these plane gravitational wave spacetimes accessible to loop quantization techniques. [ABSTRACT FROM AUTHOR]

In this paper, we discuss quantisation of cosmological tensor perturbations in the Kasner–de Sitter (KdS) space-time as a model of (pre-)inflation. Quantisation in such an anisotropic background has been argued to be problematic based on the fact that the initial Kasner singularity, where the spatial anisotropy blows up, causes divergences to the effective frequencies squared for the perturbations, which render the standard quantisation procedure relying on the existence of an adiabatic vacuum state inexecutable. Here, an essential aspect of the problem is that the ability in determining the quantum spectra of the fields is restricted. Without its knowledge, one cannot even choose physically favourable states like the Bunch–Davies vacuum in de Sitter. We here argue that this difficulty may be circumvented if only there is a period, even if temporal, after the singularity where certain adiabatic conditions for the fields are met and the standard procedure of second quantisation can be carried out within the framework of the WKB approximation. We demonstrate that our prescription for determining the quantum energy spectrum is useful in making physically meaningful predictions for the primordial gravitational waves (PGWs) in triaxially anisotropic KdS backgrounds. We confirm that, on short wave-length scales, the resulting spectrum and directional distribution of the PGWs are the same as de Sitter inflation, namely, scale invariant and isotropic. [ABSTRACT FROM AUTHOR]

We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a potential barrier. The dipole or quadrupole moment is represented by an oscillator in the relative coordinate of two constituent particles of the object. The center of mass degrees of freedom of the object is not directly coupled with the radiation field. However, we show that, for the object with the oscillator in the excited state, dissipation caused by the radiation field can suppress its quantum tunneling rate in the center of mass degrees of freedom. In addition, when the initial energy of its center of mass motion is similar to that of the excited state of the oscillator, a spatial superposition state of the object prepared by the barrier can decohere due to the radiation field. The main purpose of this article is to investigate how two different interplays (i) among the center of mass, the relative coordinate degrees of freedom and the potential barrier, and (ii) between the relative coordinate degrees of freedom and the radiation field, can affect the quantum tunneling and the creation of the spatial superposition state of the object. Our toy model can give insight into tests of quantum tunneling and quantum superposition of atoms or molecules with its dipole or quadrupole moment coupled with the radiation field. [ABSTRACT FROM AUTHOR]

We derive the pure spin connection and constraint-free BF formulations of real four-dimensional Lorentzian vacuum general relativity. In contrast to the existing complex formulations, an important advantage is that they do not require the reality constraints that complicate quantization. We also consider the corresponding modified gravity theories and point out that, contrary to their self-dual analogues, they are not viable because they necessarily contain ghosts. In particular, this constrains the set of potentially viable unified theories one can build by extending the gauge group to the ones with the action structure of general relativity. We find, however, that the resulting theories do not admit classical solutions. This issue can be solved by introducing extra dynamical fields which, incidentally, could also provide a way to include a matter sector. [ABSTRACT FROM AUTHOR]

We revise the classical continuum formulation behind the spin foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation of the ‘volume’ part of simplicity constraints, required for the passage from the topological BF theory to gravity. The crucial role, played by 4D normals in the linear version of constraints, necessitates the extension of the configuration space, and we argue to switch from normal three-forms directly to tetrads. The requirement of vanishing torsion leads to consider first an unconstrained extended Poincaré BF theory, which we characterize fully both at the Lagrangian and Hamiltonian levels, paying special attention to its gauge symmetries. The simplicity constraints are introduced naturally, in the spirit of Plebański formulation, and we give their tetradic version, dual to that of using three-forms. This brings us much closer to the geometric content of general relativity. [ABSTRACT FROM AUTHOR]

We study the quantum corrections on the Szekeres system in the context of canonical quantization in the presence of symmetries. We start from an effective point-like Lagrangian with two integrals of motion, one corresponding to the Hamiltonian and the other to a second rank killing tensor. Imposing their quantum version on the wave function results to a solution which is then interpreted in the context of Bohmian mechanics. In this semiclassical approach, it is shown that there is no quantum corrections, thus the classical trajectories of the Szekeres system are not affected at this level. Finally, we define a probability function which shows that a stationary surface of the probability corresponds to a classical exact solution. [ABSTRACT FROM AUTHOR]

The spectral dimension measures the dimensionality of a space as witnessed by a diffusing random walker. Within the causal dynamical triangulations approach to the quantization of gravity (Ambjørn et al 2000 Phys. Rev. Lett. 85 347, 2001 Nucl. Phys. B 610 347, 1998 Nucl. Phys. B 536 407), the spectral dimension exhibits novel scale-dependent dynamics: reducing towards a value near 2 on sufficiently small scales, matching closely the topological dimension on intermediate scales, and decaying in the presence of positive curvature on sufficiently large scales (Ambjørn et al 2005 Phys. Rev. Lett. 95 171301, Ambjørn et al 2005 Phys. Rev. D 72 064014, Benedetti and Henson 2009 Phys. Rev. D 80 124036, Cooperman 2014 Phys. Rev. D 90 124053, Cooperman et al 2017 Class. Quantum Grav. 34 115008, Coumbe and Jurkiewicz 2015 J. High Energy Phys. JHEP03(2015)151, Kommu 2012 Class. Quantum Grav. 29 105003). I report the first comprehensive scaling analysis of the small-to-intermediate scale spectral dimension for the test case of the causal dynamical triangulations of 3-dimensional Einstein gravity. I find that the spectral dimension scales trivially with the diffusion constant. I find that the spectral dimension is completely finite in the infinite volume limit, and I argue that its maximal value is exactly consistent with the topological dimension of 3 in this limit. I find that the spectral dimension reduces further towards a value near 2 as this case’s bare coupling approaches its phase transition, and I present evidence against the conjecture that the bare coupling simply sets the overall scale of the quantum geometry (Ambjørn et al 2001 Phys. Rev. D 64 044011). On the basis of these findings, I advance a tentative physical explanation for the dynamical reduction of the spectral dimension observed within causal dynamical triangulations: branched polymeric quantum geometry on sufficiently small scales. My analyses should facilitate attempts to employ the spectral dimension as a physical observable with which to delineate renormalization group trajectories in the hope of taking a continuum limit of causal dynamical triangulations at a nontrivial ultraviolet fixed point (Ambjørn et al 2016 Phys. Rev. D 93 104032, 2014 Class. Quantum Grav. 31 165003, Cooperman 2016 Gen. Relativ. Gravit. 48 1, Cooperman 2016 arXiv:1604.01798, Coumbe and Jurkiewicz 2015 J. High Energy Phys. JHEP03(2015)151). [ABSTRACT FROM AUTHOR]

Though loop quantization of several spacetimes has exhibited existence of a bounce via an explicit evolution of states using numerical simulations, the question about the way central singularity is resolved in the black hole interior has remained open. The quantum Hamiltonian constraint in loop quantization turns out to be a finite difference equation whose stability is important to understand to gain insights on the viability of the underlying quantization and resulting physical implications. We take first steps towards addressing these issues for a loop quantization of the Schwarzschild interior recently given by Corichi and Singh. Von-Neumann stability analysis is performed using separability of solutions as well as a full two dimensional quantum difference equation. This results in a stability condition for black holes which have a very large mass compared to the Planck mass. For black holes of smaller masses evidence of numerical instability is found. In addition, stability analysis for macroscopic black holes leads to a constraint on the choice of the allowed states in numerical evolution. States which are not sharply peaked in accordance with this constraint result in instabilities. With the caveat of using kinematical norm, sharply peaked Gaussian states are evolved using the quantum difference equation and singularity resolution is obtained. A bounce is found for one of the triad variables, but for the other triad variable singularity resolution amounts to a non-singular passage through the zero volume. States are found to be peaked at the classical trajectory for a long time before and after the singularity resolution, and retain their semi-classical character across the zero volume. Our main result is that quantum bounce occurs in loop quantized Schwarzschild interior at least for macroscopic black holes. Instability of small black holes which can be a result of using kinematical norm nevertheless signifies the need of further understanding of the viability of the considered quantization and its physical Hilbert space. [ABSTRACT FROM AUTHOR]

We extend the foliation-based quantization scheme of Park (2015 Eur. Phys. J. C 75 459) to arbitrary asymptotically flat backgrounds including those that are time- and position- dependent. One of the ingredients to accomplishing the extension is imposition of a Neumann-type boundary condition. The quantization procedure, especially the gauge-fixing-induced reduction, provides a new insight into the black hole information paradox. The hypersurface degrees of freedom in the asymptotic region—whose dynamics should be responsible for part of the ‘hair’—as well as transitions among various excitations play a central role in the global formulation of the information and proposed solution of the information paradox. In retrospect, the quantization scheme reveals the origin of the difficulty of the information problem: the problem’s ties with the quantization of gravity and subtle boundary dynamics as well as the multilayered techniques required for its setup and study. We also comment on the implications of the asymptotic symmetries for the present quantization framework. [ABSTRACT FROM AUTHOR]

Variables for constraint free null canonical vacuum general relativity are presented which have simple Poisson brackets that facilitate quantization. Free initial data for vacuum general relativity on a pair of intersecting null hypersurfaces has been known since the 1960s. These consist of the ‘main’ data which are set on the bulk of the two null hypersurfaces, and additional ‘surface’ data set only on their intersection 2-surface. More recently the complete set of Poisson brackets of such data has been obtained. However the complexity of these brackets is an obstacle to their quantization. Part of this difficulty may be overcome using methods from the treatment of cylindrically symmetric gravity. Specializing from general to cylindrically symmetric solutions changes the Poisson algebra of the null initial data surprisingly little, but cylindrically symmetric vacuum general relativity is an integrable system, making powerful tools available. Here a transformation is constructed at the cylindrically symmetric level which maps the main initial data to new data forming a Poisson algebra for which an exact deformation quantization is known. (Although an auxiliary condition on the data has been quantized only in the asymptotically flat case, and a suitable representation of the algebra of quantum data by operators on a Hilbert space has not yet been found.) The definition of the new main data generalizes naturally to arbitrary, symmetryless gravitational fields, with the Poisson brackets retaining their simplicity. The corresponding generalization of the quantization is however ambiguous and requires further analysis. [ABSTRACT FROM AUTHOR]

In this paper we consider the issue of massive gravity from a pure field theoretical point of view, as the massive deformation of the gauge theory for a symmetric rank-2 tensor field. We look for the most general massive theory with well defined propagators, imposing the absence of unphysical poles. We find several possibilities, depending on the choice of the gauge fixing term. Amongst these, two solutions with good massless limit are found. The request of the absence of tachyons, alone, does not isolate the Fierz–Pauli case: several examples of massive theories, which may or may not include the Fierz–Pauli mass term, are given. On the other hand, the Fierz–Pauli theory can be uniquely identified by means of a symmetry: it turns out the the Fierz–Pauli massive gravity is the only element of the cohomology of a BRS operator. [ABSTRACT FROM AUTHOR]

Unruh effect is a landmark prediction of standard quantum field theory in which Fock vacuum state appears as a thermal state with respect to a uniformly accelerating observer. Given its dependence on trans-Planckian modes, Unruh effect is often considered as an arena for exploring a candidate theory of quantum gravity. Here we show that Unruh effect disappears if, instead of using Fock quantization, one uses polymer quantization or loop quantization, the quantization method used in loop quantum gravity. Secondly, the polymer vacuum state remains a vacuum state even for the accelerating observer in the sense that expectation value of number density operator in it remains zero. Finally, if experimental measurement of Unruh effect is ever possible then it may be used either to verify or rule out a theory of quantum gravity. [ABSTRACT FROM AUTHOR]

For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum constraints, which maps the kinematic Hilbert space into the physical Hilbert space . Under this projection, a quantum Cauchy surface isomorphically represents a physical subspace with a kinematic subspace . The isomorphism induces the complete sets of Dirac observables in , which faithfully represent the corresponding complete sets of self-adjoint operators in . Due to the constraints, a specific subset of the observables would be ‘frozen’ as number operators, providing a background physical time for the rest of the observables. Therefore, a proper foliation with the quantum Cauchy surfaces may provide an observer frame describing the physical states of spacetimes in a Schrödinger picture, with the evolutions under a specific physical background. A simple model will be supplied as an initiative trial. [ABSTRACT FROM AUTHOR]

We develop a new framework for constructing the quantum observables of theories invariant under global time reparametrizations. Our starting point is a generalised Hamilton–Jacobi formalism for totally constrained systems. Our end result is a quantum formalism that simultaneously preserves: (i) genuine evolution; and (ii) the constraint structure of the classical formalism in the semi-classical limit. We thus offer a novel resolution of the ‘problem of time’ for theories invariant under global time reparametrization. There is the potential for the application of our proposal to the quantization of gravity when understood in terms of the Shape Dynamics formalism. [ABSTRACT FROM AUTHOR]

The loop quantization of the Schwarzschild interior region, as described by a homogeneous anisotropic Kantowski–Sachs model, is re-examined. As several studies of different—inequivalent—loop quantizations have shown, to date there exists no fully satisfactory quantum theory for this model. This fact poses challenges to the validity of some scenarios to address the black hole information problem. Here we put forward a novel viewpoint to construct the quantum theory that builds from some of the models available in the literature. The final picture is a quantum theory that is both independent of any auxiliary structure and possesses a correct low curvature limit. It represents a subtle but non-trivial modification of the original prescription given by Ashtekar and Bojowald. It is shown that the quantum gravitational constraint is well defined past the singularity and that its effective dynamics possesses a bounce into an expanding regime. The classical singularity is avoided, and a semiclassical spacetime satisfying vacuum Einstein’s equations is recovered on the ‘other side’ of the bounce. We argue that such a metric represents the interior region of a white-hole spacetime, but for which the corresponding ‘white hole mass’ differs from the original black hole mass. Furthermore, we find that the value of the white hole mass is proportional to the third power of the starting black hole mass. [ABSTRACT FROM AUTHOR]

We investigate the response of an Unruh–DeWitt detector coupled to a polymer quantized massless scalar field in flat spacetime, using the propagator obtained by Hossain, Husain and Seahra. As this propagator violates Lorentz invariance, frames moving at different constant velocities are no longer equivalent. This means that it is possible in principle for even an observer moving at constant velocity to detect radiation. We show that such an observer indeed detects radiation. Remarkably, we show that the rate of this radiation does not decrease with the decrease in the characteristic length scale of polymer quantization. Thus the radiation cannot be suppressed by making the polymer length scale arbitrarily small. Our results should bring this theory within the ambit of low-energy experiments and place a lower limit on the characteristic polymer length scale. [ABSTRACT FROM AUTHOR]

We present a Lorentz gauge theory of gravity in which the metric is not dynamical. Spherically symmetric weak field solutions are studied. We show that this solution contains the Schwarzschild spacetime at least to the first order of perturbation. Next, we present a special case of the theory where the Schwarzschild metric is an exact solution. It is also shown that the de Sitter space is an exact vacuum solution of this special case and as a result the theory is able to explain the expansion of the universe with no need for dark energy. Within this special case, quantization of the theory is also studied, the basic Feynman diagrams are derived and the renormalizability of the theory is studied using the power-counting method. We show that under a certain condition the theory is power-counting renormalizable. [ABSTRACT FROM AUTHOR]

We study the Fock quantization of a compound classical system consisting of point masses and a scalar field. We consider the Hamiltonian formulation of the model by using the geometric constraint algorithm of Gotay, Nester and Hinds. By relying on this Hamiltonian description, we characterize in a precise way the real Hilbert space of classical solutions to the equations of motion and use it to rigorously construct the Fock space of the system. We finally discuss the structure of this space, in particular the impossibility of writing it in a natural way as a tensor product of Hilbert spaces associated with the point masses and the field, respectively. [ABSTRACT FROM AUTHOR]

We exhibit a relation between the SU(2) invariant matrix model arising from the quantization of the 11-dimensional supermembrane in the light cone gauge and supersymmetric quantum cosmology. We use a Dirac-like gamma matrix representation for the fermionic degrees of freedom and find explicit solutions to reduced lower dimensional SU(2) matrix models for the zero energy states. One of the solutions we encounter in the matrix model resembles exactly a wave function found independently in the context of SUSY quantum cosmology; this allows us to give these regularized models a physical meaning and shows a direct relation between the SU(2) matrix model and SUSY quantum cosmology. [ABSTRACT FROM AUTHOR]