广义Spinfoams
Generalized Spinfoams
摘要：
我们重新考虑spinfoam动力学，最近推出的，在广义Kaminski-Kisielowski-Lewandowski（KKL）的版本，泡沫是不是双重的三角。我们研究欧几里德以及洛伦兹的情况。我们发现，这个理论仍然可以得到一个约束BF理论满足简单性约束，现在离散化的一般面向2-细胞复杂。这个限制意味着边界状态允许多面体的（量子）几何解释，推广了单纯情况下的四面体几何。我们还指出，这个约束的一般解决方案（施加弱）依赖于一个量子数r_f除了那些圈量子引力。当r_f=0时，我们计算顶点振幅，恢复出欧氏理论中的KKL振幅.我们评论的最终物理相关的r_f，和正式的方式来消除它。
英文摘要：
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.
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