Related papers: The quantum space-time of c=-2 gravity
Recent numerical results on the fractal structure of two-dimensional quantum gravity coupled to $c=-2$ matter are reviewed. Analytic derivation of the fractal dimensions based on the Liouville theory and diffusion equation is also…
In these lectures we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.
We study phases and fractal structures of three-dimensional simplicial quantum gravity by the Monte-Carlo method. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution…
We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving…
After recalling the concept of the Hausdorff dimension, we study the fractal properties of a quantum particle path. As a novelty we consider the possibility for the space where the particle propagates to be endowed with a…
We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for $-2 \leq c \leq 1$. We reformulate Q-state Potts model into the model which can be identified as a weighted…
A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of…
In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in…
We have pursued in the literature a fractal-like structure for the fractional quantum Halll effect-FQHE which consider the Hausdorff dimension associated with the quantum mechanics paths and the spin of the particles or quasiparticles…
We study the Hausdorff dimension of the path of a quantum particle in non-commutative space-time. We show that the Hausdorff dimension depends on the deformation parameter $a$ and the resolution $\Delta x$ for both non-relativistic and…
In this paper, we prove the identity $\dim_{\textrm H}(F)=d\cdot \dim_{\textrm H}(\alpha^{-1}(F))$, where $\dim_{\textrm H}$ denotes Hausdorff dimension, $F\subseteq \mathbb{R}^d$, and $\alpha:[0,1]\to [0,1]^d$ is a function whose…
We show that universal functions play an important role in the observation of the fractal structure of space--time in the numerical simulation of quantum gravity.
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central…
The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential fall off of the 2-point function with geodesic distance determines the fractal dimension $d_H$ of space-time. The integral of…
The lengths of shortest non-contractible loops are studied numerically in 2d Euclidean quantum gravity on a torus coupled to conformal field theories with central charge less than one. We find that the distribution of these geodesic lengths…
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective…
In this manuscript we explicitly compute the effective dimension of spacetime in some backgrounds of Ho\v{r}ava-Lifshitz (H-L) gravity. For all the cases considered, the results are compatible with a dimensional reduction of the spacetime…
We calculate the Hausdorff dimension, $d_H$, and the correlation function exponent, $\eta$, for polymerized two dimensional quantum gravity models. If the non-polymerized model has correlation function exponent $\eta_0 >3$ then…