Related papers: Measure in the 2D Regge quantum gravity
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular,…
The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In…
In a recent paper, we introduced a new discretization scheme for gravity in 2+1 dimensions. Starting from the continuum theory, this new scheme allowed us to rigorously obtain the discrete phase space of loop gravity, coupled to…
Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for…
In this paper we suggest gauge invariant discretization of Poincare quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewize linear Riemann-Cartan…
A comparative analysis of the versions of quantum measure in the area tensor Regge calculus is performed on the simplest configurations of the system. The quantum measure is constructed in such the way that it reduces to the Feynman path…
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…
We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalise to the…
Recent models for discrete euclidean quantum gravity incorporate a sum over simplicial triangulations. We describe an algorithm for simulating such models in general dimensions. As illustration we show results from simulations in four…
Using the Radon-Nikodym theorem concerning the relation between any two measures, as well as the methods employed in loop quantum gravity, it is shown that, in gravitation, one can quantize any measure which is not even associated with…
We re-examine the approach to four-dimensional Euclidean quantum gravity based on the Regge calculus. A cut-off on the link lengths is introduced and consequently the gravitational coupling and the cosmological constant become independent…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the…
In quantum Regge calculus areas of timelike triangles possess discrete spectrum. This is because bivectors of these triangles are variables canonically conjugate to orthogonal connection matrices varying in the compact group. (The scale of…
A theory which achieves a complete geometrical unification of gravitation and electromagnetism (GUGE) is presented. This new theory is based on a recent proposal of proper time redefinition that leads to the construction of a Riemann…
Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneously satisfies the (weak) Cartan structure equations and the…