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 canonical approach to quantum gravity has been put on a firm mathematical foundation
in the recent decades. Even the quantum dynamics can be rigorously defined, however, due …

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 …

A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity
and holography, situate areas as their fundamental variables. However, this choice of …

The first computation of a spin foam dynamics that provides a test of the quantum equations
of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is …

We study the expectation value of a nonplanar Wilson graph operator in SL (2, C) Chern–
Simons theory on S 3. In particular we analyze its asymptotic behavior in the double-scaling …

Effective spin foams provide the computationally most efficient spin foam models yet and are
therefore ideally suited for applications eg to quantum cosmology. We provide here the first …

We employ the methods of discrete (Lorentzian) Regge calculus for analysing Lorentzian
quantum cosmology models with a special focus on discrete analogues of the no-boundary …

Quantum fluctuations of the metric provide a decay mechanism for black holes, through a
transition to a white hole geometry. Old perplexing results by Ambrus and H\'aj\'i\v {c} ek and …