We survey earlier results on factorizations of extremal projectors and relative extremal projectors and present preliminary results on non-commutative factorizations of relative extremal projectors: we deduce the existence of such factorizations for sl(4) and sl(5).
Quantum gravity is the missing piece in our understanding of the fundamental
interactions today. Given recent observational breakthroughs in gravity,
providing a quantum theory for what lies beyond general relativity is more
urgent than ever. However, the complex history of quantum gravity and the
multitude of available approaches can make it difficult to get a grasp of the
topic and its main challenges and opportunities. We provide a guided tour of
quantum gravity in the form of 30 questions, aimed at a mixed audience of
learners and practitioners. The issues covered range from basic motivational
and background material to a critical assessment of the status quo and future
of the subject. The emphasis is on structural issues and our current
understanding of quantum gravity as a quantum field theory of dynamical
geometry beyond perturbation theory. We highlight the identification of quantum
observables and the development of effective numerical tools as critical to
future progress.
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 new models for four dimensional quantum
gravity. The models are motivated by a suitable implementation of the path
integral quantization of the Plebanski formulation of gravity on a simplicial
regularization. The article also includes a self-contained treatment of the 2+1
gravity. The simple nature of the latter provides the basis and a perspective
for the analysis of both conceptual and technical issues that remain open in
four dimensions.
This survey focuses on the computational complexity of some of the
fundamental decision problems in 3-manifold theory. The article discusses the
wide variety of tools that are used to tackle these problems, including normal
and almost surfaces, hierarchies, homomorphisms to finite groups, and
hyperbolic structures.
A recent article [Nature 612, 51-55 (2022)] claims to observe traversable
wormhole dynamics in an experiment. This claim is based upon performing a
teleportation protocol using a Hamiltonian that...
Lectures notes + cool videos