Calin Galeriu
We present an elegant derivation of the Doppler factor in the Lienard-Wiechert potentials of an extended particle, based on a theorem authored by J. L. Synge and dealing with cross-sections through worldtubes.
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A self-consistent consideration of the Lienard-Wiechert solition is given including its heuristic deduction, which involves a future light cone (thus the lightlike propagation of information from an arbitrarily moving pointlike charge), and physical interpretation of this field via application of three distinct reference frames (of an inertial observer, then a non-inertial one retardedly co-moving with the charged source, and finally, co-moving with the electromagnetic field). In the last frame the magnetic part of the Lienard-Wiechert field identically (though not asymptotically) vanishes in …
Retarded electromagnetic potentials are derived from Maxwell's equations and the Lorenz condition. The difference found between these potentials and the conventional Liénard-Wiechert ones is explained by neglect, for the latter, of the motion-dependence of the effective charge density. The corresponding retarded fields of a point-like charge in arbitary motion are compared with those given by the formulae of Heaviside, Feynman, Jefimenko and other authors. The fields of an accelerated charge given by the Feynman are the same as those derived from the Liénard-Wiechert potentials but not those g…
We present an in depth analysis and a new derivation of the Doppler factor in the Lienard-Wiechert potentials, based on geometrical considerations in Minkowski space. We argue that, contrary to a common assumption, the methods used for deriving the Doppler factor in the case of an electrically charged extended particle are not applicable in the case of a point particle. A geometrical interpretation of the Doppler factor is nonetheless found in the later case, based on the electromagnetic interaction model of Fokker. In this model the interaction takes place between infinitesimal worldline segm…
The illusion of acceleration in the retarded Lienard-Wiechert electromagnetic field
本文指出推迟李纳-维谢尔场对源加速度的依赖是幻象，真实电磁作用为时间对称且仅依赖位置与速度，加速度差异通过超前源改变洛伦兹力。
Lienard-Wiechert Potentials due to a 'classically' spinning point-charge in Non-Relativistic arbitrary motion
本文推导了非相对论任意运动下“经典”自旋点电荷的Lienard-Wiechert势，表明考虑转动效应与因果性后，LW势表达式中将出现包含自旋角动量的额外修正项。
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. That current includes, apart from the well-established delta-function term which is sufficient for its global conservation, additional contributions depending on the second and third proper-time derivatives of the position. These extra contributions are necessary for the local conservation of that current, whose divergence must vanish {identically} even if it is a distribution, as is the case here. Similarly, the field strength includes an additional delta-l…
Calculating the electromagnetic field of a uniformly accelerated charged particle is a surprisingly subtle problem that has been long discussed in the literature. While the correct field has been obtained many times and through various means, it remains somewhat unclear why the (supposedly general) field expression derived from the Liénard-Wiechert potentials misses some terms. We present new derivations of the missing field and potential terms by considering only pure hyperbolic motion, and we amend the offending step in the standard Liénard-Wiechert construction.
The algebraic origin of the Doppler factor in the Lienard-Wiechert potentials
该研究通过分析狄拉克δ函数恒等式推导、格林函数方法的叠加原理及Schwarzschild-Tetrode-Fokker作用量的两种表述，指出电动力学中狄拉克δ函数应为弱定义，电磁相互作用发生在粒子世界线的无穷小线段间，揭示了李纳-维谢尔势中多普勒因子的代数起源。
In 19th century Maxwell derived Maxwell equations from the knowledge of three experimental physical laws: the Coulomb's law, the Ampere's force law and Faraday's law of induction. However, theoretical basis for Ampere's force law and Faraday's law remains unknown to this day. Furthermore, the Lorentz force is considered as experimental phenomena, the theoretical foundation of this force is still unknown. To answer these fundamental theoretical questions, we derive Lienard Wiechert potentials, Maxwell's equations and Lorentz force from two simple postulates: (a) when all charges are at rest the…
The aim of this paper is to investigate the fundamental problems of retardation and radiation caused by non-uniformly moving point sources using the theories of electrodynamics and elastodynamics. This paper investigates and compares the retarded electromagnetic fields and the retarded elastodynamic fields. For the non-uniform motion of a general point source, the Liénard-Wiechert type potentials and the radiation and nonradiation fields are derived for a point charge and for a point force.
The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Liénard-Wiechert potentials. The exact closed-form solutions of the displacement and elastic fields produced by the point force and line forces are calculated. The displacement fields can be identified with the elastodynamic Liénard-Wiechert tensor potentials. For a non-uniformly moving point force, we decompose the elastic fields into a radiation part and a non-radiation part. We…
The purpose of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space-dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key-formulae for the dynamics of dislocations are …
In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables ($Q_i^2=0, Q_iQ_j\ne 0$), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the radiation gauge as phase space functions, because the difference among retarded, advanced, and symmetric Green functions is of order Q_i^2. By working in the rest-frame instant form of dynamics, the elimination of the electromagnetic degrees of freedom by means of suitable second classs contraints leads to the identification of the Lienard-Wiechert reduced phase…
It is assumed that the Lienard-Wiechert fields of an arbitrary moving charge is measured or predefined as a function of time. The position of the charge is calculated as a function of the retarded time.
Reply to Comment on "Doppler signature in electrodynamic retarded potentials"
本文回应Calin Galeriu对电动力学推迟势中多普勒特征研究的评论，修正记号错误并澄清相关形式问题。
The presence of the term $\left(\case{v}{c}\right)$ that characterizes the electrodynamic retarded potentials, also known as Liénard-Wiechert potentials, is thought to be reminiscent of a Doppler effect. Here, we show that these potentials are consistent with the Doppler shifted electromagnetic (e.m.) field generated by a charge moving along a generic trajectory with respect to the laboratory reference frame. Of course, the retarded potentials derived here are formally the same as those reported in the current literature. Nonetheless, this work sheds a new light on the origin of the electrodyn…
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. The current density includes, apart from the well-established three-dimensional delta-function which is sufficient for its global conservation, additional delta-contributions depending on the second and third proper-time derivatives of the position, which are necessary for its local conservation as required by the internal consistency of classical electrodynamics which implies that local charge-conservation is an {identity}. Similarly, the field strength inc…
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