The modular geometry of Random Regge Triangulations

The conformal geometry of Random Regge Triangulations

Moduli space intersection duality between Regge surfaces and 2D dynamical triangulations

Deformation theory for 2-dimensional dynamical triangulations with N0 vertices is discussed by exploiting the geometry of the moduli space of Euclidean polygons. Such an analysis provides an explicit connection among Regge surfaces, dynamical triangulations theory and the Witten-Kontsevich model. In particular we show that a natural set of Regge measures and a triangulation counting of relevanc...

Dynamical Regge Calculus as Lattice Quantum Gravity

We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean spacetime. In addition, lattice diffeomorphisms as invariance of the simplicial geometry are generated by certain elementary moves in the model. We attempt also a l...

Fat Triangulations and Differential Geometry

We study the differential geometric consequences of our previous result on the existence of fat triangulations, in conjunction with a result of Cheeger, Müller and Schrader, regarding the convergence of Lipschitz-Killing curvatures of piecewise-flat approximations of smooth Riemannian manifolds. A further application to the existence of quasiconformal mappings between manifolds, as well as an e...

Simplicial Quantum Gravity on a Randomly Triangulated Sphere

We study 2D quantum gravity on spherical topologies employing the Regge calculus approach with the dl/l measure. Instead of the normally used fixed non-regular triangulation we study random triangulations which are generated by the standard Voronoi-Delaunay procedure. For each system size we average the results over four different realizations of the random lattices. We compare both types of tr...