Related papers: A new realization of quantum geometry
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
We give a review of recent work aimed at understanding the dynamics of gravitational collapse in quantum gravity. Its goal is to provide a non-perturbative computational framework for understanding the emergence of the semi-classical…
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…
A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain…
The Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large…
In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense,…
Quantum matrix geometry is the underlying geometry of M(atrix) theory. Expanding upon the idea of level projection, we propose a quantum-oriented non-commutative scheme for generating the matrix geometry of the coset space $G/H$. We employ…
Quantum Geometry (the modern Loop Quantum Gravity using graphs and spin-networks instead of the loops) provides microscopic degrees of freedom that account for the black-hole entropy. However, the procedure for state counting used in the…
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the…