相关论文: Mathematical structure of loop quantum cosmology

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity programme, and is…

In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…

Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…

A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…

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…

We study the polymeric nature of quantum matter fields using the example of a Friedmann-Lemaitre-Robertson-Walker universe sourced by a minimally coupled massless scalar field. The model is treated in the symmetry reduced regime via…

We evaluate the physical viability and logical strength of an array of putative criteria for big bang singularity resolution in quantum cosmology. Based on this analysis, we propose a mutually consistent set of constitutive conditions,…

The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is…

General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…

In this contribution we consider the issue of singularity resolution within loop quantum cosmology (LQC) for different homogeneous models. We present results of numerical evolutions of effective equations for both isotropic as well as…

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…

Some long standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big bang singularity in loop…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

Over the last three years, a number of fundamental issues in quantum gravity were addressed in the framework of quantum geometry, discussed extensively by John Baez in this conference. In particular, these include: A statistical mechanical…

Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…

The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is…

In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc elements such as unphysical matter. The same…

Loop quantum cosmology is a symmetry-reduced application of loop quantum gravity that has led to the resolution of classical singularities such as the big bang, and those at the center of black holes. This can be seen through numerical…

General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…