Related papers: Quantum geometry and quantum dynamics at the Planc…
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance…
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…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
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.…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
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…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible…
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…
In recent years several ideas for experimental searches of effects induced by quantum properties of space-time have been discussed. Some of these ideas concern the role in quantum spacetime of the ordinary Lorentz symmetry of classical flat…
After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…