Related papers: A symmetric scalar constraint for loop quantum gra…
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…
We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint…
We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of…
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…
After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact gauge symmetries on the discrete level.…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…
Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum…
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a…
We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be…
We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\mathcal{H}$ into a tensor product of factors, we…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wavefunctions based on the Vassiliev knot invariants.…
We investigate the quantum area operator in the loop approach based on the Lorentz covariant hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines…
This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss the issues…