论文标题
空间量的分区功能
Partition function for a volume of space
论文作者
论文摘要
我们考虑将空间区域希尔伯特空间的维度和固定适当体积的量子分区函数计算出空间区域的希尔伯特空间的维度，并以领先顺序的鞍点近似值进行评估。结果是与马鞍球边界区域相关的Bekenstein-Hawking熵的指数，并且在有效的场理论中可靠，只要球边界处的轻度曲率奇异性受到较高的曲率项调节。这概括了De Sitter熵的经典长臂猿计算，以实现宇宙恒定和不受约束的体积的情况，因此在通用的有限空间中表现出非扰动量子重力的全息性质。
We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and is reliable within effective field theory provided the mild curvature singularity at the ball boundary is regulated by higher curvature terms. This generalizes the classic Gibbons-Hawking computation of the de Sitter entropy for the case of positive cosmological constant and unconstrained volume, and hence exhibits the holographic nature of nonperturbative quantum gravity in generic finite volumes of space.
