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In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
We present different continuous models of random geometry that have been introduced and studied in the recent years. In particular, we consider the Brownian map, which is the universal scaling limit of large planar maps in the…
In this paper, we aim to interpret the background gravitational effects appearing in quantum field theory on curved space-time by studying the Brownian motion of quantum states along with the Hamilton-Perelman Ricci flow. It has been shown…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate…
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
Based on a recent paper by Takhtajan, we propose a formulation of 2D quantum gravity whose basic object is the Liouville action on the Riemann sphere $\Sigma_{0,m+n}$ with both parabolic and elliptic points. The identification of the…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial…
A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks, and an interpretation of…
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…
We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. We…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in…