Related papers: Mathematical Structure of Loop Quantum Cosmology: …
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…
Lie algebroids provide a natural medium to discuss classical systems, however, quantum systems have not been considered. In aim of this paper is to attempt to rectify this situation. Lie algebroids are reviewed and their use in classical…
Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…
In the recent article Phys. Rev. D 100, no. 4, 043533 (2019) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and…
Chamseddine and Mukhanov recently proposed a modified version of general relativity that implements the idea of a limiting curvature. In the spatially flat, homogeneous, and isotropic sector, their theory turns out to agree with the…
We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…
One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a…
The philosophy of the Loop Quantum Gravity approach is to construct the canonical variables by using the duality of infinitesimal connections and holonomies along loops. Based on this fundamental property for example the holonomy-flux…
Projective structures have successfully been used for the construction of measures in the framework of loop quantum gravity. In the present paper, we establish such structures for the configuration space $\mathbb{R}\sqcup…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem…
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
The dynamics of a (3 + 1) dimensional homogeneous anisotropic universe is modified by Loop Quantum Cosmology and, consequently, it has generically a big bounce in the past instead of a big-bang singularity. This modified dynamics can be…
Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely…