Related papers: Canonical quantization of non-commutative holonomi…
We propose a new, discretized model for the study of 3+1-dimensional canonical quantum gravity, based on the classical $SL(2,\C)$-connection formulation. The discretization takes place on a topological $N^3$- lattice with periodic boundary…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…
Loop quantum gravity is based on a classical formulation of 3+1 gravity in terms of a real SU(2) connection. Linearization of this classical formulation about a flat background yields a description of linearised gravity in terms of a {\em…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional…
In this paper we construct the Hamiltonian constraint operator of loop quantum cosmology using holonomies defined for arbitrary irreducible SU(2) representations labeled by spin J. We show that modifications to the effective semi-classical…
In the context of quantum gravity for spacetimes of dimension 2+1, we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R^2 (representing loops on the…
We introduce the Quantum Holonomy-Diffeomorphism *-algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical…
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be…
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…
In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate…
The abstract quantum algebra of observables for 2+1 gravity is analysed in the limit of small cosmological constant. The algebra splits into two sets with an explicit phase space representation;~one set consists of $6g-6$ {\it commuting}…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
We analyze the classical limit of kinematic loop quantum gravity in which the diffeomorphism and hamiltonian constraints are ignored. We show that there are no quantum states in which the primary variables of the loop approach, namely the…
In this article we propose a new construction of the spatial scalar curvature operator in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a…
A new family of coherent states for all dimensional loop quantum gravity are proposed, which is based on the generalized twisted geometry parametrization of the phase space of $SO(D+1)$ connection theory. We prove that this family of…
We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as…
This paper constructs an approximate sinusoidal wave packet solution to the equations of loop quantum gravity (LQG). There is an SU(2) holonomy on each edge of the LQG simplex, and the goal is to study the behavior of these holonomies under…
We study the properties of $\hat{Q}[\omega]$ operator on the kinematical Hilbert space ${\cal H}$ for canonical quantum gravity. Its complete spectrum with respect to the spin network basis is obtained. It turns out that $\hat{Q}[\omega]$…