This article reviews the present status of the spin-foam approach to the quantization of
gravity. Special attention is payed to the pedagogical presentation of the recently-introduced …

The goal of this review is to present an introduction to loop quantum gravity—a background-
independent, non-perturbative approach to the problem of unification of general relativity …

Quantum gravity poses the problem of merging quantum mechanics and general relativity,
the two great conceptual revolutions in the physics of the twentieth century. The loop and …

The problem of describing the quantum behavior of gravity, and thus understanding
quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this …

We extend the definition of the “flipped” loop-quantum-gravity vertex to the case of a finite
Immirzi parameter γ. We cover both the Euclidean and Lorentzian cases. We show that the …

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined
through state sums of causal triangulated geometries, possesses a large-scale limit in which …

We give a brief overview of the properties of a higher-dimensional generalization of matrix
model which arise naturally in the context of a background approach to quantum gravity, the …

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs
are dual to higher dimensional topological spaces. The perturbative development of the …

Abstract Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has
matured over the past fifteen years to a mathematically rigorous candidate quantum field …

We review aspects of loop quantum gravity in a pedagogical manner, with the aim of
enabling a precise but critical assessment of its achievements so far. We emphasize that the …