相关论文: Discreteness of area and volume in quantum gravity

To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In the series of papers, we will introduce a graphical method, developed by Yutsis and Brink, to loop…

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…

I discuss the role played by the spin-network basis and recoupling theory (in its graphical tangle-theoretic formulation) and their use for performing explicit calculations in loop quantum gravity. In particular, I show that recoupling…

2+1 gravity coupled to a massless scalar field has an initial singularity when the spatial slices are compact. The quantized model is used here to investigate several issues of quantum gravity. The spectrum of the volume operator is studied…

The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical…

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…

Gauge-invariant observables for quantum gravity are described, with explicit constructions given primarily to leading order in Newton's constant, analogous to and extending constructions first given by Dirac in quantum electrodynamics.…

We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to…

We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…

We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian…

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of…

We investigate up to which extend the kinematic setting of loop quantum gravity can be fit into a diffeomorphism invariant setting of algebraic QFT generalizing the Haag-Kastler setting of Wightman type QFT. The net of local (Weyl-)algebras…

We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1/2) is studied in detail and applied to the non-perturbative…

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…

An alternative expression for the length operator in loop quantum gravity is presented. The operator is background independent, symmetric, positive semidefinite, and well defined on the kinematical Hilbert space. The expression for the…

We examine spectrum of the physical volume operator within the non-standard loop quantum cosmology. The spectrum is discrete with equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of…

We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…