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 …

We introduce a coarse-graining transformation for tensor networks that can be applied to
study both the partition function of a classical statistical system and the Euclidean path …

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 …

We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at
both kinematical and dynamical level, in terms of a Fock space of spin networks, and show …

We discuss how to formulate lattice gauge theories in the tensor-network language. In this
way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge …

We discuss the hints for the disappearance of continuum space and time at microscopic
scale. These include arguments for a discrete nature of them or for a fundamental non …

Tensor network contraction is central to problems ranging from many-body physics to
computer science. We describe how to approximate tensor network contraction through …

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 …

Spin foams provide path integrals for quantum gravity, which employ discretizations as
regulator. To obtain regulator independent predictions, we must remove these fiducial …