洛伦兹量子宇宙学的维度（不）依赖性
Dimensional (In)dependence of Lorentzian Quantum Cosmology
- RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））
- Graduate School of Science and Engineering, Saitama University（埼玉大学理工学研究科）
- Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University（大阪公立大学大阪中央高级数学研究所（OCAMI））
- Department of Physics, College of Humanities and Sciences, Nihon University（日本大学人文科学部物理学系）
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息研究中心）
- Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过洛伦兹路径积分和Picard-Lefschetz理论，在德西特迷你超空间近似下研究D维时空的量子宇宙跃迁振幅，发现隧穿提议在三维、四维、五维及大D极限中普遍成立，表明基于爱因斯坦引力的量子宇宙学具有跨维度普适性。
AI中文摘要：
我们在爱因斯坦引力框架下的德西特迷你超空间近似中，研究了$D$维时空中量子宇宙的跃迁振幅。结合洛伦兹路径积分与Picard-Lefschetz理论，我们识别了对积分有贡献的鞍点，并在狄利克雷边界条件下推导出良定义的跃迁振幅。我们进一步通过数值方法证明，基于Borel-Padé求和的重整化分析能有效解决某些情况下出现的残余Stokes歧义。通过分析三维、四维和五维情形以及大$D$极限，我们发现隧穿提议在宇宙从无到有的创生中普遍实现。这一结果暗示了基于爱因斯坦引力的量子宇宙学在不同维度间具有普遍特征。
英文摘要：
We study transition amplitudes of the quantum universe in $D$-dimensional spacetime within the de Sitter minisuperspace approximation in Einstein gravity. Using the Lorentzian path integral combined with Picard-Lefschetz theory, we identify the saddle points that contribute to the integral and derive a well-defined transition amplitude under Dirichlet boundary conditions. We further show numerically that a resurgence analysis based on Borel-Padé resummation is effective in resolving the residual Stokes ambiguities that arise in certain cases. Analyzing three-, four-, and five-dimensional cases, as well as the large-$D$ limit, we find that the tunneling proposal is commonly realized for the creation of the universe from nothing. This result implies a universal feature of quantum cosmology based on Einstein gravity across dimensions.
