标题： 具有有限Immirzi参数的LQG顶点 显示英文标题

标题： LQG vertex with finite Immirzi parameter

摘要： 我们将“翻转”圈量子引力顶点的定义扩展到Immirzi参数有限的情况。 我们涵盖了欧几里得情况以及洛伦兹情况。 我们证明了所得的动力学是在一个与圈量子引力相同的希尔伯特空间上定义的，并且面积算符具有与圈量子引力中相同的离散谱。 这包括对Immirzi参数的正确依赖关系，并且值得注意的是，在洛伦兹情况下也成立。 最初为了推导翻转顶点而需要的临时翻转辛结构，在Immirzi参数有限的情况下不再需要。 这些结果在四维的规范圈量子引力和自旋泡沫形式主义之间建立了一座桥梁。 显示英文摘要

摘要： We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter. We cover the Euclidean as well as the Lorentzian case. We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on the Immirzi parameter, and, remarkably, holds in the Lorentzian case as well. The ad hoc flip of the symplectic structure that was initially required to derive the flipped vertex is not anymore needed for finite Immirzi parameter. These results establish a bridge between canonical loop quantum gravity and the spinfoam formalism in four dimensions.