量子力学和引力作为四维几何的排除原理

NHEG力学：近视界极值几何（热）动力学定律

NHEG Mechanics: Laws of Near Horizon Extremal Geometry (Thermo)Dynamics

近视界极值几何（Near Horizon Extremal Geometries，NHEG）是具有$ SL(2,R) \times U(1)^N $（对于某个N）对称性的引力理论的解，是光滑的几何，并且没有事件视界，不像黑洞。根据R. M. Wald，我们推导出NHEG动力学定律，类似于NHEG的黑洞动力学定律。尽管在NHEG中没有视界，人们可以将熵与NHEG联系起来，作为诺特-瓦尔德守恒荷。我们得到了熵和熵微扰律，它们分别是对应于NHEG的守恒Noether荷和探测NHEG的系统之间的普遍关系。我们的熵定律与森的熵函数密切相关。我们还讨论了NHEG动力学定律能否由黑洞热力学定律在极值极限下得到。

Small Spins of Primordial Black Holes from Random Geometries: Bekenstein-Hawking Entropy and Gravitational Wave Observations

Black hole entropy is a robust prediction of quantum gravity with no established phenomenological consequences to date. We use the Bekenstein-Hawking entropy formula and general-relativistic statistical mechanics to determine the probability distribution of random geometries uniformly sampled in phase space. We show that this statistics (in the limit $\hbar\to 0$) is relevant to large curvature perturbations, resulting in a population of primordial black holes with zero natal spin. In principle, the identification of such a population at LIGO, Virgo, and future gravitational wave observatories…

From Quantum Codes to Gravity: A Journey of Gravitizing Quantum Mechanics

In this note, I review a recent approach to quantum gravity that "gravitizes" quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also has promise in emerging gravity in near-flat geometries.

$T\overline{T}$ in AdS$_2$ and Quantum Mechanics

Quantum field theory in zero spatial dimensions has a rich infrared landscape and a universal ultraviolet, inverting the usual Wilsonian paradigm. For holographic theories this implies a rich landscape of asymptotically AdS$_2$ geometries. Isolating the interiors of these spacetimes suggests a study of the analog of the $T\overline{T}$ deformation in quantum mechanics, which we pursue here. An equivalent description of this deformation in terms of coupling to worldline gravity is proposed, and applications to quantum mechanical systems - including the Schwarzian theory - are studied.

FLRW几何中的形变量子化

Deformation quantization in FLRW geometries

该研究将形变量子化应用于FLRW几何中的自由粒子，推导出含曲率的半经典方程，分析维格纳分布演化，揭示量子力学与宇宙膨胀的相互作用。

Horizon Quantum Mechanics of Rotating Black Holes

The Horizon Quantum Mechanics is an approach that was previously introduced in order to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended Horizon Quantum Mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavour extremal (macroscopic)…

Fuzzballs and Microstate Geometries: Black-Hole Structure in String Theory

The black-hole information paradox provides one of the sharpest foci for the conflict between quantum mechanics and general relativity and has become the proving-ground of would-be theories of quantum gravity. String theory has made significant progress in resolving this paradox, and has led to the fuzzball and microstate geometry programs. The core principle of these programs is that horizons and singularities only arise if one tries to describe gravity using a theory that has too few degrees of freedom to resolve the physics. String theory has sufficiently many degrees of freedom and this na…

引力、二次、牵引子、外尔不变性与六维量子力学

Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics

费曼和格雷厄姆在不久前指出，四维共形几何可以用六维的、周围的、允许闭同素的黎曼几何来分析。最近，它表明如何保形几何提供了一个描述的物理显然不变的单位系统的局部选择。引人注目的是，爱因斯坦的方程等价于平行标度牵引器的存在（一个在四维时空中的每一点都服从一定的一阶协变不变条件的六分量矢量）。这些结果反映了两次Bars物理计划所提出的四维物理的六维描述。费曼-格雷厄姆结构依赖于一个三元组的运营商，分别对应于一个弯曲的六维光锥，膨胀发电机和拉普拉斯算子。这些形式的sp（2）代数酒吧雇用作为第一类代数的约束在六维规范理论。本文将两种时间方法和牵引力方法相结合，将四维引力重新转换为六维量子力学。这个重力的“母体”公式是从一组无限的六维场建立起来的。成功地整合出这些领域产生各种新的描述重力，包括一个新的四维一个建立从标量二重态，拖拉机矢量多重态和共形类的度量。

曲面上的量子力学

Quantum Mechanics on Curved Hypersurfaces

在这项工作中，薛定谔和狄拉克方程将在几何学中进行检查，将粒子限制在超曲面上。为此，将考虑两种方法。第一种方法是薄层方法，它依赖于明确使用的几何关系和压缩的空间（或时空）的某一坐标。第二个是狄拉克的量子化过程，涉及利用几何约束的正则量子化的修改。对于狄拉克方程，只考虑第一种方法。最后，将比较两种方法的结果，并对结果之间的差异做一些说明。

Horizon Quantum mechanics: spherically symmetric and rotating sources

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in f…

双曲型超材料的量子力学：量子时间模型和Everett普适波函数

Quantum Mechanics of Hyperbolic Metamaterials: Modeling of Quantum Time and Everett's Universal Wavefunction

变换光学和电磁超材料的现代进步使得极不寻常的曲线光学空间的实验演示成为可能，例如电磁隐身所需的各种几何形状。最近，我们证明了在双曲超材料中映射光强度也可以在有效的（2+1）维闵可夫斯基时空中模拟时间的流动。弯曲这样一个有效的时空创造了一个玩具大爆炸的实验模型。在这里，我们证明，在低光水平，这个模型可以用来模拟一个完全协变版本的量子力学在（2+1）维闵可夫斯基时空。当在玩具大爆炸附近应用量子力学描述时，自然产生了Everett普适波函数形式，其中模型宇宙的波函数表现为相互正交的平行宇宙态的量子叠加。

量子时空的广义量子力学

Generalizing Quantum Mechanics for Quantum Spacetime

熟悉的教科书量子力学假设一个固定的背景时空来定义类空表面上的态以及它们之间的幺正演化。量子理论随着我们对空间和时间概念的发展而改变。但对于时空几何起伏不定且无定值的量子引力，量子力学需要进一步推广。本文综述了宇宙时空几何的四维、历史求和、广义量子力学。这种推广是在广义量子理论的框架内构建的。这是从封闭系统的现代量子力学中抽象出来的量子理论的最小原则集，最常见的是宇宙。在这种推广中，类空表面上的场态及其幺正演化是适合于时空几何近似经典行为的涌现性质。广义量子理论的原理允许进一步的推广，如果时空不是基本的，这将是必要的。出现的时空现象进行了一般性的讨论，并说明了与大的类空表面，从“无边界”的宇宙波函数的经典时空几何的例子。它们必须是具有一个且只有一个时间方向的洛伦兹。文章最后提出了量子力学本身是否是突现的问题。

几何力学和引力中的Clifford和Riemann-Finsler结构

Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity

这本书包含了一个收集的工作黎曼-嘉当和度量仿射流形提供非线性连接结构和广义芬斯勒-拉格朗日和嘉当-汉密尔顿几何和克利福德结构建模等流形。所提出的材料的选择已经从现代重力和几何力学中的各种应用以及对非对易黎曼-芬斯勒几何的某些推广中演变而来。本文发展和应用了具有非线性连接结构的非完整框架方法，并将其应用于一些具体问题：构造一般非对角精确解，一般具有非平凡挠率和非度量性，具有非对易对称性，描述了黑椭球/环面构形，局部各向异性虫洞，引力孤子和翘曲因子，并研究了这些解的稳定性; Lagrange/ Finsler -仿射空间的分类;非完整狄拉克算子的定义及其在交换和非交换Finsler几何中的应用。