As explained in Chapter 1, loop quantum gravity has provided a rigorous nonperturbative
framework, in which to formulate the dynamics of quantum gravity. It allowed fascinating …

Tensor network techniques have proved to be powerful tools that can be employed to
explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of …

One of the most pressing issues for loop quantum gravity and spin foams is the construction
of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for …

Higher gauge theories play a prominent role in the construction of 4D topological invariants
and have been long ago proposed as a tool for 4D quantum gravity. The Yetter lattice model …

In many quantum gravity approaches, the cosmological constant is introduced by deforming
the gauge group into a quantum group. In three dimensions, the quantization of the Chern …

In this article, we apply background-independent renormalization group methods to spin
foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion …

Simplicity constraints play a crucial role in the construction of spin foam models, yet their
effective behavior on larger scales is scarcely explored. In this article we introduce …

We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and
Freidel-Krasnov (EPRL-FK) spin foam model in the large-j limit. The vertex amplitude is …

Three-dimensional (3D) loop quantum gravity with a vanishing cosmological constant can
be related to the quantization of the SU (2) BF theory discretized on a lattice. At the classical …

A bstract We study the one-loop partition function of 3D gravity without cosmological
constant on the solid torus with arbitrary metric fluctuations on the boundary. To this end we …