Related papers: Geometrical measurements in three-dimensional quan…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
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 present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime,…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
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 investigate the relation between measurements and the physical observables for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with vanishing cosmological constant. By considering an observer who emits lightrays that…
Topological quantum field theories containing matter fields are constructed by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$ chiral (antichiral) multiplets lead to topological sigma models while $N=2$ twisted…
We develop a geometric approach to spin networks with Heisenberg or XX coupling. Geometry is acquired by defining a distance on the discrete set of spins. The key feature of the geometry of such networks is their Gauss curvature $\kappa$,…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation,…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…