Related papers: The two-vertex model of loop quantum gravity: anis…
We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and $\pi$-solitons are predicted. The second…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding…
First, we review the $C^\ast$-algebraic foundations of loop quantization, in particular, the construction of quantum configuration spaces and the implementation of symmetries. Then, we apply these results to loop quantum gravity, focusing…
Within the context of loop quantum gravity there are several operators which measure geometry quantities. This work examines two of these operators, volume and angle, to study quantum geometry at a single spin network vertex - ``an atom of…
The coefficient of the dimensionally regularized two-loop R^3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced…
In the presence of spacetime boundaries, diffeomorphisms in gravitational theories can become physical and acquire non-vanishing Noether charges. These charges obey an algebra which, within the extended phase-space formalism, faithfully…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class…
The cosmological behavior associated to a U(N)-symmetry reduced sector of the loop-quantum-gravity truncation known as the two-vertex model is further explored in this work. We construct convenient frame bases that encode the whole…
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…
After introducing the covariant phase space calculus, Noether's theorems are discussed, with particular emphasis on Noether's second theorem and the role of gauge symmetries. This is followed by the enunciation of the theory of asymptotic…
The quantum geometry arising in Loop Quantum Gravity has been known to semi-classically lead to generalizations of length-geometries. There have been several attempts to interpret these so called twisted geometries and understand their role…
In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to…
We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of…
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…