论文标题
布朗在希尔伯特（Hilbert
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
论文作者
论文摘要
在本文中，我们旨在通过研究量子态的布朗态运动以及汉密尔顿 - 佩雷尔曼·里奇（Hamilton-Perelman Ricci）的流程来解释量子场理论对弯曲时空中出现的背景引力效应。已经表明，维纳措施自动包含爱因斯坦 - 希尔伯特的作用和标量量子场理论在局部近似的一阶时标量量子场理论的路径综合公式。这为在重力的存在下提供了量子场理论的路径综合度量的明确定义的公式。但是，我们确定爱因斯坦 - 希尔伯特作用的出现与物质场相互作用无关，而仅仅是源自宇宙几何形状Ricci流的性质的熵/几何效应。我们还根据RICCI流动和汉密尔顿定理提取一个明确的公式，以实现3个manifolds。然后，我们通过RICCI流的衍生方程讨论LAMBDACDM模型中FLRW解的宇宙学特征。我们还争论了我们的配方与重力的熵方面之间的相关性。最后，我们提供了一些理论证据，证明热力学的第二定律是重力的基本来源，并且可能是一个更基本的概念。
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.
