Spin Foam Perturbation Theory for Three-Dimensional Quantum Gravity

Understand

We formulate the spin foam perturbation theory for three-dimensional Euclidean Quantum Gravity with a cosmological constant.

• We analyse the perturbative expansion of the partition function in the dilute-gas limit and we argue that the Baez conjecture stating that the number of possible distinct topological classes of perturbative configurations is finite for the set of all triangulations of a manifold, is not true.
• However, the conjecture is true for a special class of triangulations which are based on subdivisions of certain 3-manifold cubulations.
• In this case we calculate the partition function and show that the dilute-gas correction vanishes for the simplest choice of the volume operator.