基于Cubulations的Holst自旋泡沫模型
The Holst Spin Foam Model via Cubulations
摘要：
自旋泡沫模型是正则圈量子引力的协变或路径积分公式的一种尝试。这种模型的构建通常依赖于作为约束BF理论的广义相对论的普列班斯基公式，并基于对单形三角剖分的离散化，这可以被视为紫外线调节器。三角测量依赖性可以通过群场论技术来消除，该技术允许对所有三角测量求和。这些模型的主要任务是正确的量子实现Plebanski约束，存在一个半经典部门实施额外的“Regge”的约束所产生的单纯三角形，并通过群场论的定义的物理内积圈量子引力。在这里，我们提出了一种新的方法来解决这些问题直接源于霍尔斯特行动的广义相对论，这也是一个适当的起点正则圈量子引力。离散化是通过流形的“cuderance”而不是三角剖分来执行的。我们给出了一个直接的解释所产生的自旋泡沫模型作为一个生成功能的物理希尔伯特空间上的n点函数在有限的监管机构。本文重点介绍的想法和任务之前，该模型可以认真对待。然而，我们的分析揭示了这个模型的一些有趣的特点：首先，它的振幅的结构不同于标准的自旋泡沫模型。第二，四元n点函数具有“Wick型”结构。第三，对简单表象的限制不会自动发生--除非人们像经典理论那样使用时间尺度。
英文摘要：
Spin foam models are an attempt for a covariant, or path integral formulation of canonical loop quantum gravity. The construction of such models usually rely on the Plebanski formulation of general relativity as a constrained BF theory and is based on the discretization of the action on a simplicial triangulation, which may be viewed as an ultraviolet regulator. The triangulation dependence can be removed by means of group field theory techniques, which allows one to sum over all triangulations. The main tasks for these models are the correct quantum implementation of the Plebanski constraints, the existence of a semiclassical sector implementing additional "Regge-like" constraints arising from simplicial triangulations, and the definition of the physical inner product of loop quantum gravity via group field theory. Here we propose a new approach to tackle these issues stemming directly from the Holst action for general relativity, which is also a proper starting point for canonical loop quantum gravity. The discretization is performed by means of a "cubulation" of the manifold rather than a triangulation. We give a direct interpretation of the resulting spin foam model as a generating functional for the n-point functions on the physical Hilbert space at finite regulator. This paper focuses on ideas and tasks to be performed before the model can be taken seriously. However, our analysis reveals some interesting features of this model: first, the structure of its amplitudes differs from the standard spin foam models. Second, the tetrad n-point functions admit a "Wick-like" structure. Third, the restriction to simple representations does not automatically occur -- unless one makes use of the time gauge, just as in the classical theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
