相关论文: Spectral geometry as a probe of quantum spacetime

We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behaviour is…

It has been shown in [1] that a class of restricted spin foam models can feature a reduced spectral dimension of space-time. However, it is still an open question how curvature affects the flow of the spectral dimension. To answer this…

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…

Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical…

Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, {\it i.e.} ambient space formalism. In quantum geometry, the conformal sector of the…

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy…

We present the first detailed study of the kinematics of free relativistic particles whose symmetries are described by a quantum deformation of the de Sitter algebra, known as $q$-de Sitter Hopf algebra. The quantum deformation parameter is…

A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…

We show that the asymptotic dynamics of three-dimensional gravity with positive cosmological constant is described by Euclidean Liouville theory. This provides an explicit example of a correspondence between de Sitter gravity and conformal…

Several approaches to quantum gravity suggest that the standard description of spacetime as probed at low-energy, with four dimensions, is replaced in the Planckian regime by a spacetime with a spectral dimension of two. The implications…

Certain aspects of three dimensional asymptotically de Sitter spaces are studied, with emphasis on the mapping between gravity observables and the representation of the conformal symmetry of the boundary. In particular, we show that…

We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short…

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume…

We consider the four-dimensional Euclidean dynamical triangulations lattice model of quantum gravity based on triangulations of $S^{4}$. We couple it minimally to a scalar field in the quenched approximation. Our results suggest a…

We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity.Both the critical coupling and various other quantities show a slow power law approach…

This article discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein's gravity,…

In the approach of Causal Dynamical Triangulations (CDT), quantum gravity is obtained as a scaling limit of a non-perturbative path integral over space-times whose causal structure plays a crucial role in the construction. After some…

We compute the quasinormal spectra for scalar, Dirac and electromagnetic perturbations of the Schwarzschild-de Sitter geometry in the framework of scale-dependent gravity, which is one of the current approaches to quantum gravity. Adopting…

We show how Gromov's spaces of bounded geometries provide a general mathematical framework for addressing and solving many of the issues of $3D$-simplicial quantum gravity. In particular, we establish entropy estimates characterizing the…