Related papers: Loop Quantum Cosmology II: Volume Operators
In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks,…
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using…
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…
The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of…
Quantum cosmology may restrict the class of gauge models which unify electroweak and strong interactions. In particular, if one studies the normalizability criterion for the one-loop wave function of the universe in a de Sitter background…
The non-diagonal Bianchi models are studied in the loop framework for their classical and quantum formulation. The expressions of the Ashtekar-Barbero-Immirzi variables and their properties are found to provide a loop quantization of these…
The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical…
The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In this way,…
Low energy spectra of isotropic quantum dots are calculated in the regime of low electron densities where Coulomb interaction causes strong correlations. The earlier developed pocket state method is generalized to allow for continuous…
Various choices of the geometry degrees of freedom as the emergent time are tested on the model of an isotropic universe with a scalar field of $\phi^2$ potential. Potential problems with each choices as well as possible applications in…
We compute the complete spectrum of the area operator in the loop representation of quantum gravity, using recoupling theory. This result extends previous derivations, which did not include the ``degenerate'' sector, and agrees with the…
The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice…
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…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
We generalize the standard model of particle physics such it displays global scale invariance. The gravitational action is also suitably modified such that it respects this symmetry. This model is interesting since the cosmological constant…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and…