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We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization," which allows one to associate a unique quantum operator with every function on a classical phase space. Using the heat kernel coherent states of Hall and Thiemann, we show how to construct operators corresponding to functions depending on holonomies and fluxes associated with a fixed graph. We construct the coherent state versions of the fundamental holonomy and flux operators, as well as the basic geometric operators of area, angle, and volume. Our calculations show that the corresponding canonical operators are recovered from the coherent state operators in the limit of large spins. [ABSTRACT FROM AUTHOR]

We present the affine coherent state quantization of the Bianchi I model. As in our previous paper on quantum theory of Friedmann models, we employ a variable associated with a perfect fluid to play a role of clock. Then we deparametrize the model. A distinctive feature, absent in isotropic models, is an extra nonholonomic constraint, which survives the deparametrization and constrains the range of physical variables. The appearance of the constraint reflects the "amplification" of singularity due to anisotropy. The quantization smoothes the extra constraint and allows quantum contracting trajectories to be smoothly transformed into expanding ones. Making use of an affine coherent state we develop a semiclassical description. Figures are included to illustrate our result. [ABSTRACT FROM AUTHOR]

We examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider the Robertson- Walker metric coupled to a perfect fluid. It is the simplest model of a gravitational collapse, and the results obtained here may serve as a useful starting point for more complex investigations in the future. We follow a quantization procedure based on affine coherent states or wavelets built from the unitary irreducible representation of the affine group of the real line with positive dilation. The main issue of our approach is the appearance of a quantum centrifugal potential allowing for regularization of the singularity, essential self-adjointness of the Hamiltonian, and unambiguous quantum dynamical evolution. [ABSTRACT FROM AUTHOR]

Evolution of systems in which Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides. We identify and study this additional structure in the framework of relational observables ("partial observables"). We formulate necessary and sufficient conditions for the resulting evolution in the physical phase space to be a symplectomorphism. We give examples which satisfy those conditions and examples which do not. We point out that several classic positions in the literature on relational observables contain an incomplete approach to the issue of evolution and false statements. Our work provides useful clarification and opens the door to studying correctly formulated definitions. [ABSTRACT FROM AUTHOR]

We develop a systematic classical framework to accommodate the canonical quantization of geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existing approach of standard cosmological perturbations is indeed proved to be good only up to first order in the inhomogeneities, and only if the background is treated classically. To consistently quantize the perturbations and the background, a new set of classical phase-space variables is required. We show that, in a natural gauge, a set of such Dirac observables exists, and their algebra is of the canonical form. Finally, we compute the physical Hamiltonian that generates the dynamics of such observables with respect to the homogeneous part of a Klein-Gordon "clock" field T. The results of this work provide a good starting point to understanding and calculating the effects that quantum cosmological spacetime in the background has on the quantum perturbations of the metric tensor and of matter fields. [ABSTRACT FROM AUTHOR]

We consider a massive quantum test Klein-Gordon field probing a homogeneous isotropic quantum cosmological space-time in the background. In particular, we derive a semiclassical space-time which emerges to a mode of the field. The method consists of a comparison between quantum field theory on a quantum background and quantum field theory on a classical curved space-time, giving rise to an emergent metric tensor (its components being computed from the equation of propagation of the quantum Klein-Gordon field in the test field approximation). If the field is massless the emergent metric is of the Friedmann-Robertson-Walker form, but if a mass term is considered it turns out that the simplest emergent metric that displays the symmetries of the system is of the Bianchi I type, deformed in the direction of propagation of the particle. This anisotropy is of a quantum nature: it is proportional to h and "dresses" the isotropic classical space-time obtained in the classical limit. [ABSTRACT FROM AUTHOR]

We develop the quantum theory of a scalar field on loop quantum cosmology Bianchi I geometry. In particular, by considering only the single modes of the field, the evolution equation is derived from the quantum scalar constraint: it is shown that the same equation can be obtained from quantum field theory on a "classical" effective geometry. We then study the dependence of this effective space-time on the wave vector of the modes (which could in principle generate a deformation in local Lorentz symmetry), by analyzing the dispersion relation for propagation of the test field on the resulting geometry. We show that when we disregard the backreaction no Lorentz violation is present, despite the effective metric being different than the classical Bianchi I. Furthermore, a preliminary analysis of the correction due to inclusion of backreaction is briefly discussed in the context of Born-Oppenheimer approximation. [ABSTRACT FROM AUTHOR]

In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made toward understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, based on results in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semiclassical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in general relativity and the common effective Hamiltonian proposed in earlier literature. [ABSTRACT FROM AUTHOR]

We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of loop quantum gravity in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and graph-preserving Hamiltonian is central, result in the formulation of a set of no-go statements, severely limiting the possibility of recovering a physically consistent effective dynamics this way. [ABSTRACT FROM AUTHOR]

In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter β in the modified dispersion relation of the modes, hence, inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015)], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context. [ABSTRACT FROM AUTHOR]

Evolution of systems in which Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides. We identify and study this additional structure in the framework of relational observables ("partial observables"). We formulate necessary and sufficient conditions for the resulting evolution in the physical phase space to be a symplectomorphism. We give examples which satisfy those conditions and examples which do not. We point out that several classic positions in the literature on relational observables contain an incomplete approach to the issue of evolution and false statements. Our work provides useful clarification and opens the door to studying correctly formulated definitions. [ABSTRACT FROM AUTHOR]