Three-Dimensional Theory

Summary
As we apply the ideas of Chapter 2 (relating two points in space-time with a Hamiltonian), Chapter 3 (the quantization of gravity), and Chapter 4 (making the models discrete) to a model of three-dimensional Euclidean space.

Section 5.1
Strategy is to construct a Hilbert space as a model for the boundary of the space (spacetime?) that we wish to model and then to construct the transition amplitude function for pairs of boundary states We use the 2-complex quantization of space (spacetime?) in which space is considered to be a 2-comlex (a space-filling collection of tetrahedra) with
 * If I have this right the wording in the book is a bit off.
 * A rotation from SU(2), $$U_e$$, associated with each edge, e. This represents the net change in orientation (the holonomy) from one vertex to the next of the geometry
 * An element of the su(2) algebra, $$L_f$$, for each face of the dual complex. This element is the net change in the triad, i.e. "spacetime", along the line segment.I think that we should allow the complex to jiggle. I sounds here as if we have fixed a background...