Related papers: Quantum Geometry II : The Mathematics of Loop Quan…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
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…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
Loop Quantum Gravity is a nonperturbative and background independent program for the quantization of General Relativity. Its underlying formalism has been applied successfully to the study of cosmological spacetimes, both to test the…
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…
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…
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…
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…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory,…
Loop Quantum Gravity is a formalism for describing the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. The most important result of LQG is that geometric quantities such as area and…
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and…
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…