Related papers: Modelling Space with an Atom of Quantum Geometry
We consider the coupling between massive and spinning particles and three dimensional gravity. This allows us to construct geometric operators (distances between particles) as Dirac observables. We quantize the system a la loop quantum…
We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the role of these operators from the Asymptotic Safety…
In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the physics of computation to ensembles of clocks, as in GPS, we present a covariant version of the…
Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…
We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…
Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed…