Related papers: Implementation of the holonomy representation of t…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the…
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…
Holonomies of the Ashtekar-Barbero connection can be considered as abstract elements of a Lie group exponentially mapped from their connections representation. This idea provides a possibility to compare the geometric and algebraic…
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that…
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…
Loop quantum gravity methods are applied to a symmetry-reduced model with homogeneity in two dimensions, derived from a Gowdy model [5,6]. The conditions for propagation of unidirectional plane gravitational waves at exactly the speed of…
In the context of the geometrical interpretation of the spin network states of Loop Quantum Gravity, we look at the holonomies of the Ashtekar-Barbero connection on loops embedded in space-like hyperboloids. We use this simple setting to…
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out.…
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by…
The procedure of the holonomy-flux algebra construction along a piecewise linear path, which consists of a countably infinite number of pieces, is described in this article. The related construction approximates the continuous distribution…
A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll's discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological…
We advocate an alternative description of canonical gravity in 3+1 dimensions, obtained by using as the basic variable a real variant of the usual Ashtekar connection variables on the spatial three-manifold. With this ansatz, no non-trivial…
In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An…
We develop an effective framework for the $\bar\mu$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory, and then…
We elaborate on the Ashtekar's formalism for spherically symmetric midisuperspaces and, for loop quantization, propound a new quantization scheme which yields a graph-preserving Hamiltonian constraint operator and by which one can impose…
In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and…