Related papers: Graphical method in loop quantum gravity: I. Deriv…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite,…
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…
In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to…
Using a new procedure based on Kummer's Confluent Hypergeometric Functions, we investigate the question of singularity avoidance in loop quantum gravity (LQG) in the context of U$(1)^3$ complexifier coherent states and compare obtained…
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…
We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann's version of the constraint and compute its action…
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.
The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
A new alternative volume operator is constructed for loop quantum gravity by using the so-called cotriad operators as building blocks. It is shown that the new volume operator shares the same qualitative properties with the standard volume…
The aim of this work is to introduce several different volume computation methods of the graph polytope associated with various type of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and…
Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very…
The volume operator is an important kinematical quantity in the non-perturbative approach to four-dimensional quantum gravity in the connection formulation. We give a general algorithm for computing its spectrum when acting on four-valent…
We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier' in two dimensional quantum gravity. We study multiple Ising models living on dynamical $\phi^3$ graphs and analyse the behaviour of…
In this article we examine a Hamiltonian constraint operator governing the dynamics of simple quantum states, whose graph consists of a single six-valent vertex, in quantum-reduced loop gravity. To this end, we first derive the action of…
This manuscript is the first in a series of instalments that investigate spherically symmetric solutions within the effective dynamics program of Loop Quantum Gravity. The choice of lattice is adapted such that it remains invariant under a…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.