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 …

In quantum gravity, we envision renormalization as the key tool for bridging the gap between
microscopic models and observable scales. For spin foam quantum gravity, which is defined …

A bstract In the tetrad formulation of gravity, the so-called simplicity constraints play a central
role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path …

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

In this paper we generalize the results of Gurau (arxiv: 1011. 2726 [gr-qc], 2011), Gurau and
Rivasseau (arxiv: 1101.4182 [gr-qc], 2011) and derive the full 1/N expansion of colored …

This book concerns the foundations of Quantum Gravity, in particular from a conceptual point
of view. It provides a self-contained introduction to this topic, resting on particular features of …

A cornerstone of the loop quantum gravity program is the fact that the phase space of
general relativity on a fixed graph can be described by a product of SU (2) cotangent …

Making the Lorentzian path integral for quantum gravity well-defined and computable has
been a long standing challenge. In this work we adopt the recently proposed effective spin …

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 …

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a
graphical calculus for the unitary representations of the Lorentz group. The asymptotics of …