More on the Thomas precession and the relativistic transformation to rotating frames
L. Herrera
我们评论的一些误解表现在最近的论文Matolcsi等人。39 413（2007））。
We comment on some misunderstandings exhibited in a recent paper by Matolcsi et al. (Gen. Rel. Grav.39 413 (2007)).
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Thomas rotation and Thomas precession
在绝对（无坐标）的狭义相对论中，给出了沿圆形世界线的托马斯旋转和托马斯岁差的精确而简单的计算。除了计算的简单性，时空的绝对处理使我们能够更深入地了解托马斯旋转和托马斯岁差现象。
Relativistic velocity space, Wigner rotation and Thomas precession
我们开发了一个相对论性的速度空间称为\emph{rapidity space}从洛伦兹不变性的单一假设，并使用它来可视化和计算所产生的效果连续应用非共线洛伦兹助推。特别是，我们展示了如何快速空间提供了一个几何方法维格纳旋转和托马斯岁差在同样的方式，时空提供了一个几何方法运动学效应在狭义相对论。
The Thomas precession and the transformation to rotating frames
托马斯进动是使用三种不同的变换来计算旋转坐标系。它示出，对于足够大的值的$v/c$，出现在预测的进动角的重要差异，这取决于所使用的变换。对于较小的$v/c$值，可以通过延长观察时间来测量这些差异。
Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact …
Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession
本文的目的是对狭义相对论中速度组合的定性和定量结果，包括维格纳旋转和托马斯进动，作一个初步的介绍。我们只使用最熟悉的狭义相对论工具，在三个不同层次上进行论证：（1）完全初级的，适合第一门相对论课程;（2）中级的，适合第二门课程;（3）高级的，适合更高层次的学生。然后，我们总结了有用的结果，并建议在这个往往晦涩的领域进一步阅读。
On the relation of Thomas rotation and angular velocity of reference frames
在处理托马斯旋转的相对论现象的大量文献中，已经开发了几种方法来计算陀螺仪沿圆形世界线的托马斯旋转角。在\cite{rindler}中引入的最吸引人的概念之一是考虑与陀螺仪共同运动的旋转参考系，并将陀螺仪的进动与参考系的角速度相关联。然而，最近的论文\cite{herrera}将这一原理应用于三个不同的同向移动旋转参考系，并得到三个不同的托马斯旋转角。出现这种明显矛盾的原因是，\cite{rindler}的原则被用于一种它并不适用的情况。在本文中，我们严格审查的理论背景和适用性的\cite{rindler}原则的限制。在此过程中，我们还建立了一些一般性质的{ \it旋转参考系}，这可能是独立的利益。
Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
本研究针对描述旋转玻色-爱因斯坦凝聚体的二维磁性非线性薛定谔能量泛函，在快速旋转极限下推导类Thomas-Fermi有效模型，通过均匀气体能量低密度展开定义与涡旋晶格相关的耦合常数。
Particles in rotating saddle potentials exhibit precessional motion which, up to now, has been explained by explicit computation. We show that this precession is due to a hidden Coriolis-like force which, unlike the standard Coriolis force, is present in the inertial frame. We do so by finding a hodograph-like "guiding center" transformation using the method of normal form.
Wigner rotations are transformations that affect spinning particles and cause the observable phenomenon of Thomas precession. Here we study these rotations for arbitrary symmetry groups with a semi-direct product structure. In particular we establish a general link between Wigner rotations and Thomas precession by relating the latter to the holonomies of a certain Berry connection on a momentum orbit. Along the way we derive a formula for infinitesimal, Lie-algebraic transformations of one-particle states.
Precession of a Freely Rotating Rigid Body. Inelastic Relaxation in the Vicinity of Poles
研究刚体自由旋转时进动现象，探讨非弹性松弛对极区稳定性的影响，揭示对称和非对称体的复杂行为及内部损耗机制。
We present an energy functional for a Thomas-Fermi type two-fluid model of a self-gravitating non-rotating charged body, with a non-relativistic kinetic energy. We prove that, under certain conditions on the total number of positively charged and negatively charged particles, a minimizer exists and both fluids have compact support. We prove the same result for special relativistic kinetic energy, assuming further conditions on the total number of particles. In the non-relativistic kinetic energy case, we further prove the uniqueness of the minimizer, as well as present results relating the gen…
A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope τ from the inertial vertical z, in uniform rate Ω_1=τΩ, and the whole tank is elevated over other table rotating at rate Ω. Under these conditions, a set of Kelvin waves is formed on the free surface depending on the angle of tilt, characterized by the slope τ, volume of water, and rotation rate. The resonant mode in the system appears in the form of a single Kelvin solitary wave, whose am…
We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our starting point is the Gross-Pitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding Thomas-Fermi quantities and we derive the next order contributions due to vortices. As an application, we consider a general potential of the …
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