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http://arxiv.org/pdf/0704.0278

q-deformed spin foam models of quantum gravity

Igor Khavkine and J. Daniel Christensen

02 April 2007

Large triangulations are necessary to approximate semiclassical space-times. The possibility of obtaining numerical results from larger triangulations takes us one step closer to that goal and increases the number of facets from which the physical properties of a spin foam model may be examined. As an example, we are able to study how the spin-spin correlation varies with the distance between faces in the triangulation.

Consider a triangulated 4-manifold. Let _n denote the set of n-dimensional simplices of the triangulation. The dual 2-skeleton is formed by associating a dual vertex, edge and polygonal face to each 4-simplex, tetrahedron, and triangle of the triangulation, respectively.

**Given the discrete structure of our spacetime model, it is conceivable that this combinatorial distance, multiplied by a fundamental unit of length,**approximates some notion of distance derived from the dynamical geometry of the spin foam model.

(I use a double tetra. See my visuals)

jal