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Here's a quick overview of the physics behind CDT:
- Spacetime is constructed using a lattices of simplices (Regge calculus)
- Simplices are n-dimensional triangles
- Curvature of a D-dimensional Delaunay lattice is concentrated on the co-dimension 2 simplices, or “bones"
- The Ricci scalar can be expressed as the deficit angle between the co-dimension 1 faces around the bones, times the Areas of the faces
- The Regge calculus equivalent of the Hilbert action is just the sum over all of the bones,
- The Einstein-Hilbert action is calculated as a discrete path integral which converges with a cosmological constant,
- The path integral is summed over all inequivalent triangulations
- There is a well-defined Wick-rotation to evaluate the path integral
- Specify initial manifold, final manifold, find all ways to fill in space
- Pachner moves + Metropolis algorithm pick out inequivalent triangulations
- Transition amplitudes calculable
- Random walk diffuser calculates spectral dimension: d at large scales, 2 at small scales
- Fixing the lengths of the edges to get the simplex area easily and increasing number of simplices is dynamical triangulation
- Enforcing causal structure leads to causal dynamical triangulations
- Pick \alpha as edge length for timelike edges and pick “ergodic” Pachner moves respecting foliation
- What are observables? Hard to extract information
Here's a recent talk I have gave about the work:
http://slides.com/acgetchell/causal-dynamical-triangulations-3
The full details may be found here:
http://arxiv.org/pdf/hep-th/0105267v1.pdf
A reading list of CDT, including foundations and latest results, may be found in this Zotero public group:
https://www.zotero.org/groups/causal-dynamical-triangulations
Finally, here's a nicely accessible blog post, written by Jonah Miller, one of my collaborators:
http://www.thephysicsmill.com/2013/10/13/causal-dynamical-triangulations/