量子态希尔伯特空间中的布朗运动、里奇流与随机涌现的爱因斯坦-希尔伯特作用量：为存在引力的量子场构造良定义的费曼路径积分测度
Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity
AI总结：
本文通过量子态沿里奇流的布朗运动，证明Wiener测度可自然涌现爱因斯坦-希尔伯特作用量，从而为弯曲时空量子场论提供良定义的路径积分测度，并论证引力源于热力学第二定律。
摘要：
在本文中，我们旨在通过研究量子态沿汉密尔顿-佩雷尔曼里奇流的布朗运动，来解释弯曲时空量子场论中出现的背景引力效应。研究表明，在局域近似的一阶项上，Wiener测度自动包含爱因斯坦-希尔伯特作用量以及弯曲时空上标量量子场论的路径积分表述。这为存在引力时的量子场论路径积分测度提供了一个良定义的表述。然而，我们确立：爱因斯坦-希尔伯特作用量的涌现与物质场相互作用无关，而仅仅是一种源于宇宙几何里奇流本质的熵/几何效应。我们还根据里奇流和三维流形的汉密尔顿定理，提取出宇宙学常数的显式公式。然后，我们通过推导出的里奇流方程，讨论了LambdaCDM模型中FLRW解的宇宙学特征。我们还论证了我们的表述与引力的熵方面之间的关联。最后，我们提供了一些理论证据，证明热力学第二定律是引力的基本来源，并且可能是一个更基本的概念。
英文摘要：
In this paper, we aim to interpret the background gravitational effects appearing in quantum field theory on curved space-time by studying the Brownian motion of quantum states along with the Hamilton-Perelman Ricci flow. It has been shown that the Wiener measure automatically contains the Einstein-Hilbert action and the path-integral formulation of the scalar quantum field theory on curved space-time at the first order of local approximations. This provides a well-defined formulation of the path-integral measure for quantum field theory in the presence of gravity. However, we establish that the emergence of Einstein-Hilbert action is independent of the matter field interactions and is a merely entropic/geometric effect stemming from the nature of the Ricci flow of the universe geometry. We also extract an explicit formula for the cosmological constant in terms of the Ricci flow and the Hamilton theorem for 3-manifolds. Then, we discuss the cosmological features of the FLRW solution in the LambdaCDM Model via the derived equations of the Ricci flow. We also argue the correlation between our formulations and the entropic aspects of gravity. Finally, we provide some theoretical evidence that proves the second law of thermodynamics is the basic source of gravity and probably a more fundamental concept.
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