Recursion relations in spin foam models

          @misc{ pirsa_PIRSA:09120011,
            doi = {10.48660/09120011},
            url = {https://pirsa.org/09120011},
            author = {Bonzom, Valentin},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Recursion relations in spin foam models},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {dec},
            note = {PIRSA:09120011 see, \url{https://pirsa.org}}
          }
          

Abstract

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.