Coarse graining dynamical triangulations: a new scheme

Abstract

A new procedure for coarse-graining dynamical triangulations is presented. The procedure provides a meaning for the relevant value of observables when "probing at large scales", e.g. the average scalar curvature. The scheme may also be useful as a starting point for a new type of renormalisation procedure, suitable for dynamically triangulated quantum gravity. Random Delaunay triangulations have previously been used to produce discretisations of continuous Euclidean manifolds, and the coarse-graining scheme is an extension of this idea, using random simplicial complexes produced from a dynamical triangulation. In order for a coarse-graining process to be useful, it should preserve the properties of the original dynamical triangulation that are relevant when probing at large scales. Some general discussion of this point is given, along with some arguments in favour of the proposed scheme.

19 pages (14 main body), 3 figures. Accepted for publication in Class. Quant. Grav

References in corpus (4)

• Spectral Dimension of the Universe
• Reconstructing the Universe
• The Nonperturbative Quantum de Sitter Universe
• Semiclassical Quantum Gravity: Statistics of Combinatorial Riemannian Geometries

Cited by in corpus (7)

• Nonperturbative Quantum Gravity
• Spectral geometry as a probe of quantum spacetime
• Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
• Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
• Measuring the Homogeneity (or Otherwise) of the Quantum Universe
• Semiclassical states in quantum gravity: Curvature associated to a Voronoi graph
• Landau Theory of Causal Dynamical Triangulations