单模量子宇宙学中的Duru-Kleinert路径积分
Duru-Kleinert Path Integral in Unimodular Quantum Cosmology
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中文总结 AI 辅助
本文采用Duru-Kleinert路径积分技术，研究单模量子宇宙学与氢原子的对应关系，推导量子化负宇宙学常数，计算宇宙从“无”的隧穿率及正宇宙学常数下的谱密度与Krylov复杂度。
中文摘要 AI 辅助
近期研究表明，在单模引力框架下，充满无压尘埃和宇宙学常数的平直Friedmann-Lemaitre-Robertson-Walker宇宙的Wheeler-DeWitt方程等价于氢原子的径向薛定谔方程。本文采用Duru-Kleinert路径积分技术，重新研究单模量子宇宙学与氢原子的对应关系。Duru-Kleinert时间重参数化将宇宙的欧几里得路径积分转化为一维库仑系统的路径积分。通过Mellin-Barnes积分表示，提取格林函数的束缚态极点，这些极点对应量子化的负宇宙学常数。我们直接在库仑模型中计算从“无”到宇宙的量子隧穿率。此外，对于正宇宙学常数，我们计算无界态的谱密度和Krylov复杂度。
英文摘要
The Wheeler-DeWitt equation of a flat Friedmann-Lemaitre-Robertson-Walker universe filled with pressureless dust and a cosmological constant in the unimodular gravity is recently shown to be equivalent to the radial Schrödinger equation of a hydrogen atom. In this paper, we revisit this correspondence between the unimodular quantum cosmology and the hydrogen atom by using the Duru-Kleinert path integration technique. The Duru-Kleinert time reparametrization transforms the Euclidean path integral of the universe into that of a one-dimensional Coulomb system. Through a Mellin-Barnes integral representation, we extract the bound state poles of the Green's function, which give the quantized negative cosmological constant. We compute the quantum tunneling rate from ``nothing'' to a universe directly within the Coulomb model. Furthermore, for a positive cosmological constant, we compute the spectral density and the Krylov complexity for the unbounded state.
发表机构
- School of Mathematics & Physics, Yancheng Institute of Technology（盐城工学院数学与物理学院）
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