Related papers: Geometrical measurements in three-dimensional quan…
Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their…
Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's…
In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the ``boundary'' of spacetime. I review what is…
We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial…
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…
Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the…
I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological role of a vector field in the framework of a string/brane cosmological model. I will then present…
We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…
Quantum geometric maps, which relate SU(2) spin networks and Lorentz covariant projected spin networks, are an important ingredient of spin foam models (and tensorial group field theories) for 4-dimensional quantum gravity. We give a…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The quantum theory of the spherically symmetric gravity in 3+1 dimensions is investigated. The functional measures are explicitly evaluated and the physical state conditions are derived by using the technique developed in two dimensional…
Gauge-invariant observables for quantum gravity are described, with explicit constructions given primarily to leading order in Newton's constant, analogous to and extending constructions first given by Dirac in quantum electrodynamics.…
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
Quantum gravity is quite elusive at the experimental level; thus a lot of interest has been raised by recent searches for quantum gravity effects in the propagation of light from distant sources, like gamma ray bursters and active galactic…
Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…
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 propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.