Spin Foams Without Spins

Understand

We formulate the spin foam representation of discrete SU(2) gauge theory as a product of vertex amplitudes each of which is the spin network generating function of the boundary graph dual to the vertex.

• In doing so the sums over spins have been carried out.
• The boundary data of each n-valent node is explicitly reduced with respect to the local gauge invariance and has a manifest geometrical interpretation as a framed polyhedron of fixed total area.
• Ultimately, sums over spins are traded for contour integrals over simple poles and recoupling theory is avoided using generating functions.