AV-微分几何与牛顿力学

Hamilton-Jacobi方程作为模型降维，扩展至牛顿粒子力学，以及一个波动力学的趣闻

Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity

本文将Hamilton-Jacobi方程视为保守粒子力学的模型降维，扩展至包含非保守力的牛顿粒子系统，并通过几何光学近似得到耗散的Schrödinger方程。

Newtonian mechanics in a Riemannian manifold

The work done by Isaac Newton more than three hundred years ago, continues being a path to increase our knowledge of Nature. To better understand all the ideas behind it, one of the finest ways is to generalize them to wider situations. In this report we make a review of one of these enlargements, the one that bears the mechanical systems from the elementary homogeneous three dimensional Euclidean space to the more abstract geometry of a Riemannian manifold.

耗散、非完整牛顿力学的变分作用量原理

Action principles for dissipative, non-holonomic Newtonian mechanics

本文提出在速度与位置一般依赖的力与约束下为牛顿力学推导对偶变分原理的方法，并给出耗散与非完整约束系统的显式示例及对偶哈密顿流和运动常数存在的条件。

从巴格曼超选择定则到量子牛顿时空

From Bargmann's superselection rule to quantum Newtonian spacetime

巴格曼超选择规则禁止不同质量态的叠加存在，因此意味着在非相对论性量子力学中不可能描述不稳定粒子。然而，通常的伽利略变换不足以描述非相对论性量子力学的对称性，因为它们未能考虑可能在波函数中产生非相对论性相位的相对论性时间收缩效应。本文描述了低速极限下Bargmann定则与洛伦兹变换之间的不相容性，分析了它的经典起源，指出推广的Galilei群更好地刻画了理论的对称性。此外，我们主张，非相对论性量子力学的正确描述需要在相应的极限中对时空概念进行修改，这只对量子粒子才是明显的。

相对论性Boltzmann方程的牛顿极限

The Newtonian limit of the relativistic Boltzmann equation

本文考虑了具有周期边界条件的常微分截面相对论Boltzmann方程。对于适当大的正$c_0$，光速表现为参数$c>c_0$。在与$c>c_0$无关的时间区间上证明了一个局部存在唯一性定理，并给出了在极限$c\to +\infty$下解在适当的范数下收敛于硬球非相对论Boltzmann方程解的条件.

通过经典声子实现量子力学代数。I：作为牛顿运动方程的薛定谔方程以及作为经典平均值的量子可观测量

Algebra of quantum mechanics via classical phonons. I: The Schrodinger equation as the Newtonian equation of motion and quantum observables as classical averages

通过经典声子模型（Frenkel-Kontorova模型）形式上得到单自旋无粒子的薛定谔方程，从耦合谐振子晶格出发经一系列变换在非相对论极限下将克莱因-戈登方程写成薛定谔方程，还能将经典可观测量重写为量子可观测量。

Spherical space in the Newtonian limit: The cosmological constant

We compute the cosmological constant of a spherical space in the limit of weak gravity. To this end we use a duality developed by the present authors in a previous work. This duality allows one to treat the Newtonian cosmological fluid as the probability fluid of a single particle in nonrelativistic quantum mechanics. We apply this duality to the case when the spacetime manifold on which this quantum mechanics is defined is given by $\mathbb{R}\times\mathbb{S}^3$. Here $\mathbb{R}$ stands for the time axis and $\mathbb{S}^3$ is a 3-dimensional sphere endowed with the standard round metric. A q…

框架独立力学：仿射丛上的几何

Frame-independent mechanics:geometry on affine bundles

介绍了仿射丛微分几何的主要思想。介绍并讨论了李代数体和Poisson结构的仿射对应。所开发的概念适用于一个独立的框架制定的时间依赖性和牛顿力学。

On the analytic representation of Newtonian systems

We show that the theory of self-adjoint differential equations can be used to provide a satisfactory solution of the inverse variational problem in classical mechanics. A Newtonian equation when transformed to the self-adjoint form allows one to find an appropriate Lagrangian representation (direct analytic representation) for it. On the other hand, the same Newtonian equation in conjunction with its adjoint provides a basis to construct a different Lagrangian representation (indirect analytic representation) for the system. We obtain the time-dependent Lagrangian of the damped Harmonic oscill…

牛顿规范下微扰弗里德曼方程的研究

On the perturbed Friedmann equations in Newtonian Gauge

本文基于牛顿力学启发式推导弗里德曼方程，并结合热力学第一定律与欧拉方程得到线性阶与广义相对论一致的微扰方程，揭示两种框架在特定极限下的一致性。