Related papers: Classical dynamics for Loop Gravity: The 2-vertex …
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…
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…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
We present a separable version of Loop Quantum Gravity (LQG) based on an inductive system of cubic lattices. We construct semi-classical states for which the LQG operators -- the flux, the area and the volume operators -- have the right…
The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which…
Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in…
The building blocks of a quantum theory of general relativity are expected to be discrete structures. Loop quantum gravity is formulated using a basis of spin networks (wave functions over oriented graphs with coloured edges), thus…
A new Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time…
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…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
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…
An open issue in loop quantum gravity (LQG) is the introduction of a non-vanishing cosmological constant $\Lambda$. In 3d, Chern-Simons theory provides some guiding lines: $\Lambda$ appears in the quantum deformation of the gauge group. The…
We show how Loop Quantum Cosmology can be derived as an effective semiclassical description of Loop Quantum Gravity. Using the tools of QRLG, a gauge fixed version of LQG, we take the coherent states of the fundamental microscopic theory…
In this study, we model a spin-network in loop quantum gravity as a regular tetrahedral lattice, applying lattice physics techniques to study its structure and vertex dynamics. Using the area eigenvalue, $A\propto 8\pi l_P^2$, we derive a…
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries…
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 intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…
We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…