Related papers: The Sum over Topologies in Three-Dimensional Eucli…
We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the…
According to the holographic principle, the maximum amount of information stored in a region of space scales as the area of its two-dimensional surface, like a hologram. We show that the holographic principle can be understood heuristically…
Euclidean quantum gravity is reconsidered, in the conformal mode approximation. Applying techniques from glass theory, we argue that the Euclidean partition function hides metastable states, which can be counted. This may reconcile…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the…
QCD and related gauge theories have a sign problem when a $\theta$-term is included; this complicates the extraction of physical information from Euclidean space calculations as one would do in lattice studies. The sign problem arises in…
Attention is focused on quantum spaces of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. Each of these quantum spaces can be…
The problem of topology change transitions in quantum gravity is investigated from the Wheeler-de Witt wave function point of view. It is argued that for all theories allowing wormhole effects the wave function of the universe is…
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…
The three-dimensional pure quantum gravity with a negative cosmological constant has been conjectured to be dual to an extremal conformal field theory (ECFT), of central charge c=24k for some positive integer k. We compute the partition…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics.…
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
We study the path integral quantization of the topological 3BF theory, whose gauge symmetry is described by a 3-group. This theory is relevant for the quantization of general relativity coupled to Standard Model of elementary particles. We…
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…
We consider a model of 3d quantum gravity defined by $n$ copies of a rational Virasoro TQFT with central charge $1/2$, summed over all 3d topologies. This theory is holographically dual to an ensemble of all 2d CFTs with central charge…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
In the quest of a physical theory of quantum gravity, spin foam models, or in short spinfoams, propose a well-defined path integral summing over quantized discrete space-time geometries. At the crossroad of topological quantum field theory,…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…