标题： 从广义相对论和量子 Friedmann 方程得出的量子力学 显示英文标题

标题： Quantum Mechanics from General Relativity and the Quantum Friedmann Equation

摘要： 我们证明了最近引入的线性方程（重新表述了第一个弗里德曼方程）是一阶WKB展开的一种宇宙学量子方程。这一结果揭示了广义相对论与量子力学之间更深层次的联系，指向一个统一的框架。该方程的解是通过包含自由下落粒子量子效应的标度因子来构建的。量子标度因子重塑了宇宙动力学，在其消失点处消除了奇异性。作为一个明确的例子，我们考虑了辐射主导时期，并表明量子方程与近期应用于黑洞的Seiberg-Witten形式中的方程是对偶的，并包含了Kontsevich、Segal和Witten发展的resurgence现象和复数度规。这与对偶波函数在$\Gamma(2)$变换下时间参数化不变性相关联。 显示英文摘要

摘要： We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General Relativity and Quantum Mechanics, pointing towards a unified framework. Solutions of this equation are built in terms of a scale factor encapsulating quantum effects on a free-falling particle. The quantum scale factor reshapes cosmic dynamics, resolving singularities at its vanishing points. As an explicit example, we consider the radiation-dominated era and show that the quantum equation is dual to the one in Seiberg-Witten formulation, recently applied to black holes, and incorporates resurgence phenomena and complex metrics, as developed by Kontsevich, Segal, and Witten. This links to the invariance of time parametrization under $\Gamma(2)$ transformations of the dual wave function.