2010/11/14 by You Ding, Muxin Han, Carlo Rovelli · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1103/physrevd.83.124020
published as Phys.Rev.D83:124020,2011 · 16 pages, 3 figures
arxiv created 2010/11/14 · arxiv updated 2011/06/27
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 rf in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when rf=0. We comment on the eventual physical relevance of rf, and the formal way to eliminate it.