Related papers: Curvature Tensor in Discrete Gravity
I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in some detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are…
We study a formulation of lattice gravity defined via Euclidean dynamical triangulations (EDT). After fine-tuning a non-trivial local measure term we find evidence that four-dimensional, semi-classical geometries are recovered at long…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
We propose a new, discretized model for the study of 3+1-dimensional canonical quantum gravity, based on the classical $SL(2,\C)$-connection formulation. The discretization takes place on a topological $N^3$- lattice with periodic boundary…
We construct numerical basis function sets on a lattice, whose spatial extension is scalable from single lattice sites to the continuum limit. They allow us to compute small and large bound states with comparable, moderate effort. Adopting…
We derive an expression for the energy-momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter (cond-mat/9502063) describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of…
Tiling spaces are constructed using a metric in which two tilings of $\mathbb{R}^n$ are close if and only if, after a small translation, they agree on a large ball around the origin. We construct analogous spaces to study random…
The local character of self-gravity along with the number of spatial dimensions are critical issues when computing the potential and forces inside massive systems like stars and disks. This appears from the discretisation scale where each…
This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
We propose a discrete lattice model of the energy of dislocations in three-dimensional crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic interatomic interactions, elastic deformations and discrete…
We introduce the linear connection in the noncommutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, define the metric connection and calculate the curvature.…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
In a 6D model, where the extra dimensions form a discretised curved disk, we investigate the mass spectra and profiles of gravitons and Dirac fermions. The discretisation is performed in detail leading to a star-like geometry. In addition,…
Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such ``discrete folding'' was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium.…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from…
A model for quantized gravitation based on the simplicial lattice discretization is studied in detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value…