标题： 退化普莱班斯基扇区和自旋泡沫量子化 显示英文标题

标题： Degenerate Plebanski Sector and Spin Foam Quantization

摘要： 我们证明了Spin(4) Plebanski形式的四维引力的退化部分是精确可解的，并且可以协变地嵌入SU(2) BF理论。这一事实确保了其自旋泡沫量子化由SU(2) Crane-Yetter模型给出，并允许测试各种施加简单性约束的方法。我们的分析强烈表明，在Spin(4) BF理论的状态和中限制表示和互化子是不足以得到正确的顶点振幅的。相反，对于一般的Plebanski类型理论，我们提出了一种量子化过程，该过程在构造上等价于规范路径积分量子化，并且应用于我们的模型时，会重现SU(2) Crane-Yetter状态和。此过程的一个特征是将次级第二类约束与初级简单性约束同等对待，这导致了顶点振幅的新公式。 显示英文摘要

摘要： We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2) Crane-Yetter model and allows to test various approaches of imposing the simplicity constraints. Our analysis strongly suggests that restricting representations and intertwiners in the state sum for Spin(4) BF theory is not sufficient to get the correct vertex amplitude. Instead, for a general theory of Plebanski type, we propose a quantization procedure which is by construction equivalent to the canonical path integral quantization and, being applied to our model, reproduces the SU(2) Crane-Yetter state sum. A characteristic feature of this procedure is the use of secondary second class constraints on an equal footing with the primary simplicity constraints, which leads to a new formula for the vertex amplitude.