Related papers: Asymptotic cones and quantum gravity
We define cone structures and asymptotic invariants for multigraded systems of ideals, and show that essentially the only restrictions on such structures is convexity, which is imposed formally.
Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the…
We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric space is bounded from below by that of any pseudo-cone of…
I discuss the notion of asymptotic safety and possible applications to quantum field theories of gravity and matter.
In the framework of the recently proposed asymptotically finite gauge models the cosmological constant is essentially weakened by quantum effects. The next (and more general) claim is that the coupling between quantum fields may suppress…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
Asymptotic Safety implies that observables including scattering amplitudes remain finite at the highest energy scales. Traditionally, this feature is connected to an interacting fixed point of the Wilsonian renormalization group that…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
We define thin and asymptotically scattered metric spaces as asymptotic counterparts of discrete and scattered metric spaces respectively. We characterize asymptotically scattered spaces in terms of prohibited subspaces, and classify thin…
Matter-quantum gravity interactions can be used for direct and also indirect experimental tests of quantum gravity. We focus on photon-photon scattering in asymptotically safe gravity as a direct test of the small-scale structure of…
I discuss some theoretical ideas concerning the representation of quantum gravity as a Lorentz-symmetry-violating `medium' with non-trivial optical properties, which include a refractive index in `vacuo' and stochastic effects associated…
We discuss some new developments in three-dimensional gravity with torsion, based on Riemann-Cartan geometry. Using the canonical approach, we study the structure of asymptotic symmetry, clarify its fundamental role in defining the…
This is an introduction to asymptotically safe quantum gravity, explaining the main idea of asymptotic safety and how it could solve the problem of predictivity in quantum gravity. In the first part, the concept of an asymptotically safe…
A possible solution to the problem of providing a spacetime description of the transmission of signals for quantum entangled states is obtained by using a bimetric spacetime structure, in which quantum entanglement measurements alter the…
Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.
Asymptotic Safety (AS) Paradigm is an interesting set of ideas and methods towards a meaningful quantization of Gravity. A brief review of phenomenological consequences in the context of AS regarding cosmology with emphasis on dark energy…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…
We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as…
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also…