Related papers: Could we observe the discreteness of Quantum-Gravi…
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indication that Planck scale geometry in LQG is discontinuous…
It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of to possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation…
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite,…
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
We investigate some properties of geometric operators in canonical quantum gravity in the connection approach \`a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous…
We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial…
We investigate the implications for the measurability of distances of a covariant dimensionful ``$\kappa$'' deformation of D=4 relativistic symmetries, with quantum time coordinate and modified Heisenberg algebra. We show that the structure…
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare algebra with associated momenta living on (a…
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive…
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and non-vanishing curvature of momentum space.…
We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the…
The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This…
A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum…
I investigate the relation between an operative definition of the area of a surface specified by matter fields and the area operators recently introduced in the canonical/loop approach to Quantum Gravity and in Rovelli's variant of the…
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…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…