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キーワード:
General Relativity and Quantum Cosmology, gr-qc
要旨:
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.
