非Noether对称群的对合轨道

Hamilton动力系统的非Noether对称性

Non-Noether symmetries in Hamiltonian Dynamical Systems

讨论了非Noether对称的几何性质及其在可积Hamilton系统中的可能应用。非Noether对称性和守恒律之间的对应关系被重新审视。本文证明了在正则Hamilton系统中，这种对称性正则地导致相空间上余切丛上线性算子代数上的一个拉克斯对。考虑了非Noether对称性与其他广泛应用的生成守恒律的几何方法如双Hamilton形式主义、双微分微积分和Frolicher-Nijenhuis几何之间的关系。证明了当连续非Noether对称性的生成元满足一定的Yang-Baxter型方程时，与连续非Noether对称性相关的运动积分是对合的.研究了单参数对称群对运动积分代数的作用，讨论了群轨道的对合性。揭示并讨论了Toda链、非线性Schrodinger方程、Korteweg-de Vries方程、Benney系统、非线性水波方程和Broer-Kaup系统的隐藏非Noether对称性。

Schwarzschild时空中粒子轨道（类时测地线）的隐藏对称群

Hidden symmetry group for particle orbits (timelike geodesics) in Schwarzschild spacetime

本文通过逆用Noether定理，为Schwarzschild时空中类时测地线方程新发现的三个隐藏守恒量（LRL角、LRL Killing矢量时间和LRL固有时）提供了自然的对称性解释，并揭示了它们与Killing对称性一起构成完整的Noether对称群。

Universal Corner Symmetry and the Orbit Method for Gravity

A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners -- codimension-$2$ surfaces supporting Noether charges. It applies to both finite distance and asymptotic corners. In this paper, we study this algebra and its representations, via the coadjoint orbit method. We show that generic orbits of the universal algebra split into sub-orbits spanned by finite distance and asymptotic corner symmetries, such that the full universal symmetry algebra gives rise to a unified treatment …

左手adelic狄拉克算子与黎曼零点的谱实现

A Chiral Adelic Dirac Operator and the Spectral Realization of the Riemann Zeros

本文提出了一种基于左手adelic狄拉克算子的框架，通过谱移位不连续性重新诠释黎曼ζ(s)非平凡零点，结合素数索引变形和有限素数截断实现算术谱流动的数值探索。

First Integrals and symmetries of nonholonomic systems

In nonholonomic mechanics, the presence of constraints in the velocities breaks the well-under\-stood link between symmetries and first integrals of holonomic systems, expressed in Noether's Theorem. However there is a known special class of first integrals of nonholonomic systems generated by vector fields tangent to the group orbits, called {\it horizontal gauge momenta}, that suggest that some version of this link should still hold. In this paper we prove that, under certain conditions on the symmetry Lie group, the (nonholonomic) momentum map is conserved along the nonholonomic dynamics, t…

Poisson gauge models and Seiberg-Witten map

The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance in the direction of a further development of the proposed formalism, including the derivation of Noether identities and conservation of currents. For any linear non-commutativity, $Θ^{ab}(x)=f^{ab}_c\,x^c$, with $f^{ab}_c$ being structure constants of a Lie algebra, an explicit form of the gauge Lagrangian is proposed. In particular a universal solution for …