Lorenz or Coulomb in Galilean Electromagnetism ?

A Note On Galilean Invariants In Semi-Relativistic Electromagnetism

The incompatibility between the Lorentz invariance of classical electromagnetism and the Galilean invariance of continuum mechanics is one of the major barriers to prevent two theories from merging. In this note, a systematic approach of obtaining Galilean invariant field variables and equations of electromagnetism within the semi-relativistic limit is reviewed and extended. In particular, the Galilean invariant forms of Poynting's theorem and the momentum identity, two most important electromagnetic identities in the thermomechanical theory of continua, are presented. In this note, we also in…

On some applications of Galilean electrodynamics of moving bodies

We discuss the seminal article in which Le Bellac and Lévy-Leblond have identified two Galilean limits of electromagnetism [1], and its modern implications. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We discuss various applications and experiments, such as in quantum mechanics, superconductivity, electrodynamics of continuous media, etc. Much of the current technology, where waves are not taken into account, is actually based on Galilean electromagnetism

关于伽利略电磁学的评论

Remarks on Galilean electromagnetism

研究展示伽利略电磁学在有源时的方程在l-共形伽利略群下保持不变，揭示了与加速框架相关的动态不稳定性。

Lorenz规范与正则电磁学中的Poisson括号

Lorenz gauge and the Poisson bracket in canonical electromagnetism

本文研究Lorenz规范下矢量势及其共轭动量的正则Poisson括号，证明规范固定后朴素括号仍因规范条件与相对性原理的协同而成立。

Galilean Covariance versus Gauge Invariance

We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known "gauge conditions" of the literature are interpreted physically as electromagnetic continuity equations hence the "gauge fields". The existence of a Galilean Electromagnetism with TWO dual limits ("electric" and "magnetic") is the crux of the problem [1]. A phase-space with the domains of validity of the various "gauge conditions" is provided and is shown to depend on three c…

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Le…