Related papers: Semiclassical analysis of the Loop Quantum Gravity…
Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
This is the third paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we analyze models which, despite the fact that the phase space is…
After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We…
The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG…
We describe the quantum flat universe in QRLG in terms of states based at cuboidal graphs with six-valent nodes. We investigate the action of the scalar constraint operator at each node and we construct proper semiclassical states. This…
We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar…
The ``problem of time'' has been a pressing issue in quantum gravity for some time. To help understand this problem, Rovelli proposed a model of a two harmonic oscillators system where one of the oscillators can be thought of as a ``clock''…
We explore the constraints following from requiring the Area Law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single link wave-function in the large j limit, believed to be appropriate…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
The standard toolkit of operators to probe quanta of geometry in loop quantum gravity consists in area and volume operators as well as holonomy operators. New operators have been defined, in the U(N) framework for intertwiners, which allow…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
A new set of twisted geometric variables is introduced to parametrize the holonomy-flux phase space in loop quantum gravity. It is verified that these new geometric variables, after symplectic reduction with respect to the Gauss constraint,…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to…
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
We analyze the spectral properties of the volume operator of Ashtekar and Lewandowski in Loop Quantum Gravity, which is the quantum analogue of the classical volume expression for regions in three dimensional Riemannian space. Our analysis…
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), {\em directly at the quantum level}. Such a firmer understanding would…
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…
We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data…