发表机构
Osaka Metropolitan University; RIKEN（大阪公立大学; 理化学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在洛伦兹量子宇宙学中精确构造了DeWitt核，通过非奇异路径求和实现边界条件，并给出了闭式解，涵盖无宇宙学常数闭合宇宙及德西特宇宙情形。
AI 中文摘要
DeWitt边界条件可以通过仅对非奇异路径求和，在迷你超空间量子宇宙学的洛伦兹路径积分中实现。我们给出了由此产生的DeWitt核的一般定义，以及构造它们的明确规则，并精确地评估了它们。正半轴上的延迟积分产生Wheeler--DeWitt算子的Dirichlet格林函数，而整个实轴上的积分产生Dirichlet群平均核；当任一端点位于奇点时，两者都消失。由于迷你超空间作用量至多是二次的，所有延迟积分都以闭式形式执行，无需鞍点近似。我们获得了没有宇宙学常数的闭合宇宙的核，其中整个实轴核恒等于零，平坦的德西特宇宙的核，以及用Airy函数表示的闭合和开放德西特宇宙的核。在整个过程中，DeWitt条件被强加为奇点处的边界条件，这选择了半轴上的自伴约束算子，并唯一地确定了核，包括它们的归一化。
英文摘要
The DeWitt boundary condition can be implemented in the Lorentzian path integral of minisuperspace quantum cosmology by summing only over non-singular paths. In this paper, we present a general definition of the resulting DeWitt kernels, along with specific rules for their construction, and evaluate them rigorously. The lapse integral over the positive half-line yields the Dirichlet Green function of the Wheeler--DeWitt operator, whereas the integral over the whole real line yields the Dirichlet group-averaging kernel; both vanish when either endpoint lies at the singularity. Since the minisuperspace actions are at most quadratic, all lapse integrals are performed in closed form without saddle-point approximations. We obtain the kernels for the closed universe without cosmological constant, for the flat de Sitter universe, and, in terms of Airy functions, for the closed and open de Sitter universes. Throughout, the DeWitt condition is imposed as the boundary condition at the singularity, which selects a self-adjoint constraint operator on the half-line and fixes the kernels uniquely, including their normalization.
Comments11 pages. v2: Minor revisions and clarifications
