This book aims to present a pedagogical and self-consistent treatment of the canonical
approach to Quantum Gravity, starting from its original formulation to the most recent …

Intertwiners are the building blocks of spin-network states. The space of intertwiners is the
quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we …

We present a nonperturbative quantization of general relativity coupled to dust and other
matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian …

This is a review of the present status of loop and spin foam approaches to quantization of
four-dimensional general relativity. It aims at raising various issues which seem to challenge …

The dual picture of quantum geometry provided by a spin network state is discussed. From
this perspective, we introduce a new operator in Loop Quantum Gravity—the length …

A consistent combination of quantum geometry effects rules out a large class of models of
loop quantum cosmology and their critical densities as they have been used in the recent …

The relation between loop quantum gravity (LQG) and tensor networks is explored from the
perspectives of the bulk-boundary duality and holographic entanglement entropy. We find …

We introduce a new framework for loop quantum gravity: mimicking the spin foam
quantization procedure we propose to study the symmetric sectors of the theory imposing …

We quantize the new connection formulation of (D+ 1)-dimensional general relativity
developed in our companion papers by loop quantum gravity (LQG) methods. It turns out …

In cosmological group field theory (GFT) models for quantum gravity coupled to a massless
scalar field the total volume, seen as a function of the scalar field, follows the classical …