Generalized spinfoams

作者：Ding You^*; Han Muxin; Rovelli Carlo

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2011, 83(12): 124020.

DOI：10.1103/PhysRevD.83.124020

We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kamin'ski-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.

• 出版日期2011-6-9