Relativistic Statistical Mechanics with Angular Momentum

论量子力学与经典电磁学和经典相对论力学的关系

On the Relationship of Quantum Mechanics to Classical Electromagnetism and Classical Relativistic Mechanics

探讨了量子力学与经典物理之间的某些联系。普朗克-爱因斯坦关系和德布罗意关系、波函数及其概率解释、正则对易关系和麦克斯韦-洛仑兹方程可以通过比较经典电磁学和经典相对论运动学对光的光子学描述而得到简单的理解。所使用的方法可以被描述为“逆对应”，因为考虑到经典电磁学的低光子数密度极限，量子现象变得明显。推广到大质量粒子，就得到了克莱因-戈登方程和薛定谔方程。比较详细地讨论了光子的量子波函数与经典电磁波的量子波函数之间的差别。

The pedagogical value of the four-dimensional picture I: Relativistic mechanics of point particles

We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of particles and fields are quite simple geometric objects as opposed to their associated three-dimensional trajectories, and (ii) Newton's second law requires neither modification nor generalization, it should be only smoothly embedded in the four-dimensional geometry of Minkowski spacetime to yield the dynamical law for relativistic particles.

Angular momenta in fields from a rotational mechanical antenna

Mechanic antennas provide opportunities for human portable, VLF communications, where a rotational dipole emits EM signals with angular momenta. In this paper we analytically derive the electromagnetic fields from a rotational electric dipole using Fourier transform method, and find that the radiated fields from the rotational electric dipole carries nonzero energy flow density in both orbital and spin angular momentum (AM) parts by AM flux tensors. Intuitively, a rotation of a dipole induces a longitudinal orbital angular momentum and a longitudinal spin angular momentum both circulating in t…

Analytical mechanics of a relativistic particle in a positional potential

We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be useful in the study of phenomenological models. Also the Dirac and Klein-Gordon equation differ from the standard formulation, with corrections of order (E-m)/m in the energy spectra.

Relativistic forces in Lagangian mechanics

We give a general definition of \emph{relativistic force} in the context of Lagrangian mechanics. Once this is done we prove that the only relativistic forces which are linear on the velocities are those coming from differential 2-forms defined on the configuration space. In this sense, electromagnetic fields provide a mechanical system with the simplest type of relativistic forces.

视觉相对论力学

Visual relativistic mechanics

本文通过双曲三角函数展示相对论概念的视觉表达，提出新的相对论火箭方程和多普勒效应推导方法。