Related papers: Mathematical structure of loop quantum cosmology
Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and technical ones to probe the consistency of…
A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of…
In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
In the last decades, progress on the quantization of black holes using techniques developed in loop quantum cosmology has received increasing attention. Due to the quantum geometry effect, the resulting quantum corrected black hole is free…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics.…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological…
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner.…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…