Related papers: Angle and Volume Studies in Quantized Space
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…
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…
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…
The choice of the area operator in loop quantum gravity is by no means unique. In addition to the area operator commonly used in loop quantum gravity there is also an area operator introduced by Krasnov in 1998, which gives uniformly spaced…
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)…
The canonical theory of quantum gravity in the loop representation can be extended to incorporate topology change, in the simple case that this refers to the creation or annihilation of "minimalist wormholes" in which two points of the…
The paper shows how the Bohmian approach to quantum physics can be applied to develop a clear and coherent ontology of non-perturbative quantum gravity. We suggest retaining discrete objects as the primitive ontology also when it comes to a…
Witten described how a path integral quantization of Wilson Loop observables will define Jones polynomial type of link invariants, using the Chern-Simons gauge theory in $\mathbb{R}^3$. In this gauge theory, a compact Lie group ${\rm G}$,…
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…
The Euclidean formulation of quantum gravity can be interpreted in terms of a probability distribution over Riemannian manifolds. In the context of de Sitter gravity, the statistics of the total volume according to this distribution is…
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…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
We study a family of physical observable quantities in quantum gravity. We denote them W functions, or n-net functions. They represent transition amplitudes between quantum states of the geometry, are analogous to the n-point functions in…
In this work, we propose a generalization of the current most widely used quantum computing hardware metric known as the quantum volume. The quantum volume specifies a family of random test circuits defined such that the logical circuit…
We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors…
Quantum gravity is sometimes considered as a kind of metaphysical speculation. In this review, we show that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an invaluable…