Talks

The scaling analysis in the large spin limit of Feynman amplitudes for the Bosonic colored group field theory are considered in any dimension starting with dimension 4. By an explicit integration of two colors, we show that the model is positive. This formulation could be useful for the constructive analysis of this type of models.

Spin foam models aim at defining non-perturbative and background independent amplitudes for quantum gravity. In this work, I argue that the dynamics and the geometric properties of spin foam models can be nicely studied using recursion relations. In 3d gravity and in the 4d Ooguri model, the topological invariance leads to recursion relations for the amplitudes. I also derive recursions from the action of holonomy operators on spin network functionals. Their geometric content is discussed in terms of elementary moves on simplices, and is related to the classical constraints of the underlying theories. Interestingly, our recurrence relations apply to any SU(2) invariant symbol. Another method is considered for non-topological objects, and applied to the 10j-symbol which defines the Barrett-Crane spin foam model.