论文标题
完整的Barrett-Crane模型及其因果结构
The Complete Barrett-Crane Model and its Causal Structure
论文作者
论文摘要
因果结构是连续时空物理学的典型元素，需要在洛伦兹量子重力理论中正确编码。建立的旋转泡沫（和张力群组田间理论（TGFT））模型主要与相对特殊的洛伦兹三角剖分（例如，仅是由空间般的四面体）构建的，从而掩盖了微观水平上局部因果关系的显式实施。我们克服了这一局限性，并为洛伦兹量子几何形状构建了一个成熟的模型，其构件包括空位般的，灯光般的和时型的四面体。我们在Barrett-Crane TGFT模型的背景下意识到这一点。在通过积分几何学方法对振幅的明确表征以及随后对局部因果结构的清晰识别进行了清晰识别，我们分析了该模型相对于其（空间）时间方向的特性的模型的幅度，并提供了与因果动力学三角形的框架（CDT）的框架。
The causal structure is a quintessential element of continuum spacetime physics and needs to be properly encoded in a theory of Lorentzian quantum gravity. Established spin foam (and tensorial group field theory (TGFT)) models mostly work with relatively special classes of Lorentzian triangulations (e.g. built from spacelike tetrahedra only), obscuring the explicit implementation of the local causal structure at the microscopic level. We overcome this limitation and construct a full-fledged model for Lorentzian quantum geometry the building blocks of which include spacelike, lightlike and timelike tetrahedra. We realize this within the context of the Barrett-Crane TGFT model. Following an explicit characterization of the amplitudes via methods of integral geometry, and the ensuing clear identification of local causal structure, we analyze the model's amplitudes with respect to its (space)time-orientation properties and provide also a more detailed comparison with the framework of causal dynamical triangulations (CDT).
