Generalized Spinfoams

You Ding (1, 2) , Muxin Han (1, 2) , Carlo Rovelli (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kaminski-Kisielowski-Lewandowski (KKL) version where the foam is not dual to a triangulation. We study the Euclidean as well as the Lorentzian case. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. This constraint implies that boundary states admit a (quantum) geometrical interpretation in terms of polyhedra, generalizing the tetrahedral geometry of the simplicial case. We also point out that the general solution to this constraint (imposed weakly) depends on a quantum number r_f in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when r_f=0. We comment on the eventual physical relevance of r_f, and the formal way to eliminate it.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

You Ding, Muxin Han, Carlo Rovelli. Generalized Spinfoams. Physical Review D, 2011, 83, pp.124020. ⟨hal-00534768⟩