Related papers: Are the spectra of geometrical operators in Loop Q…

The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the…

We define a modification of LQG in which graphs are required to consist in piecewise linear edges, which we call piecewise linear LQG (plLQG). At the diffeomorphism invariant level, we prove that plLQG is equivalent to standard LQG, as long…

Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…

This letter is motivated by the recent papers by Dittrich and Thiemann and, respectively, by Rovelli discussing the status of Quantum Geometry in the dynamical sector of Loop Quantum Gravity. Since the papers consider model examples, we…

A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…

Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…

In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…

In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are…

There is a precise sense in which the requirement of background independence suffices to uniquely select the kinematics of loop quantum gravity (LQG). Specifically, the fundamental kinematic algebra of LQG admits a unique diffeomorphism…

We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of 1. the Brown -- Kuchar…

Differences between vector potentials in different gauges contain no dynamics in both classical and quantum electrodynamics and chromodynamics. Consequently, once gauge invariance is established, results calculated in non-covariant gauges…

Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…

We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a…

Remarkably we find that for a ring with linear boundary conditions such that the eigenvector and its derivative are continuous, there does not seem to be a way for the well-known de Broglie relation to be gauge invariant. Certain nonlinear…

Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…

In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian…

Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite.…

In this paper we investigate the properties of gauge-invariant coherent states for Loop Quantum Gravity, for the gauge group U(1). This is done by projecting the corresponding complexifier coherent states, which have been applied in…

The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG…

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…