Related papers: Asymptotic cones and quantum gravity
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
This paper is a sequel to the series of papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033, gr-qc/9704038, gr-qc/9708014, gr-qc/9802016, gr-qc/9802022]. We define a quantum measurement as a…
A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different…
Asymptotic Safety is a promising framework towards the understanding, in a non-perturbative way, of Quantum Gravity. It treats the Newton's constant G_N and the cosmological constant \Lambda as running coupling of an effective action. At…
Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $\Gamma$ be a uniform lattice in G. (a) If $CH$ holds, then $\Gamma$ has a unique asymptotic cone up to…
We consider a massive quantum test Klein-Gordon field probing an isotropic quantum cosmological space-time in the background. The result obtained is surprising. It turns out, that despite the isotropy of the quantum gravitational field, the…
In this paper, we first prove that any power quasi-symmetry of two metric spaces induces a rough quasi-isometry between their infinite hyperbolic cones. Second, we prove that for a complete metric space $Z$, there exists a point $\omega$ in…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
The issue of whether some manifestations of gravitation in the quantum domain, are indicative or not of a non-geometrical aspect in gravitation is discussed. We examine some examples that have been considered in this context, providing a…
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…
Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a non-zero cosmological constant $\Lambda$ in this context has been a withstanding problem. Other approaches, such as Chern-Simons gravity, suggest…
A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of…
Quantum gravity is sometimes considered as a kind of metaphysical speculation. In this review, we show that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an invaluable…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
We introduce the notion of negative topological dimension and the notion of weight for the asymptotic topological dimension. Quantizing of spaces of negative dimension is applied to linguistic statistics.
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…
Quantum asymmetry is a physical resource which coincides with the amount of coherence between the eigenspaces of a generator responsible for phase encoding in interferometric experiments. We highlight an apparently counter-intuitive…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…