V. Hnizdo, G. Vaman
The self-force of a point charge moving on a rectilinear trajectory is obtained, with no need of any explicit removal of infinities, as the negative of the time rate of change of the momentum of its retarded self-field.
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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。
A Galilean invariant description of the retarded electric interaction of two moving charges is carried out, considering the EM action to propagate at the speed of light. Through the altering of the Liénard-Wiechert potential (LWP) a new retarded, electric potential called retarded Coulomb potential (RCP) is ordered to the moving charges. RCP depends on the velocities both of the interacting charges. The force law of the electric interaction of moving charges is determined by means of the second order approximation of RCP. The force law obtained is the Galilean invariant Webers force law, surpr…
A short proof that the Coulomb-gauge potentials yield the retarded fields
本文简要地论证了库仑规范中的势产生滞后的电场和磁场。这个演示相对简单，可以在电磁理论的高级本科课程中提出，
Quantum electrodynamics and experiment demonstrate the non-retarded nature of electrodynamical force fields
在量子电动力学中，科学史上最成功的定量理论，遵循平方反比定律的电荷间力是由于类空间虚光子的交换。基本的量子过程的基础应用，如电子和电机的旋磁比，则是莫勒散射$ee \to ee$。对这个过程的量子振幅的分析表明，相应的电荷间力是瞬时作用的。这一预测在最近的一项实验中得到了验证。
In this work, the theory of second gradient electrodynamics, which is an important example of generalized electrodynamics, is proposed and investigated. Second gradient electrodynamics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian density. Second gradient electrodynamics possesses a weak nonlocality in space and time. In the framework of second gradient electrodynamics, the retarded Green functions, first-order derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, gen…
Maxwell's electrodynamics postulates the finite propagation speed of electromagnetic (EM) action and the notion of EM fields, but it only satisfies the requirement of the covariance in Minkowski metric (Lorentz invariance). Darwin's force law of moving charges, which originates from Maxwell's field theory complies the Lorentz invariance as well. Poincaré's principle stating that physical laws can be formulated with identical meaning on different geometries suggest, that the retarded EM interaction of moving charges might be covariant even in Euclidean geometry (Galilean invariance). Keeping th…
Criticism of "Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics" by Andrew E. Chubykalo and Stoyan J. Vlaev
证明了由Lienard-Wiechert势导出的电磁场不满足麦克斯韦方程组的证明是错误的。在计算延迟量的导数时出现了错误。不能作出瞬时和延迟电磁相互作用的必然性的后续推论。不同的规范选择可以导致标量势和矢量势的各种形式，但总是具有相同的延迟场。经典电磁理论是完整的，正如通常所表达的那样。人们可以选择在洛伦兹规范中工作，在那里所有的量都是滞后的。
In this paper, we investigate the so-called Bopp-Podolsky electrodynamics. The Bopp-Podolsky electrodynamics is a prototypical gradient field theory with weak nonlocality in space and time. The Bopp-Podolsky electrodynamics is a Lorentz and gauge invariant generalization of the Maxwell electrodynamics. We derive the retarded Green functions, first derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strengths in the framework of the Bopp-Podolsky electrodyn…
Retarded electric and magnetic fields of a moving charge: Feynman's derivation of Liénard-Wiechert potentials revisited
从麦克斯韦方程组和洛伦兹条件推导出延迟电磁势。这些电位和传统的Liénard-Wiechert电位之间的差异可以通过忽略有效电荷密度的运动依赖性来解释。本文将任意运动的点状电荷的相应延迟场与Heaviside、Feynman、Jefimenko等人的公式作了比较。由费曼给出的加速电荷的场与由Liénard-Wiechert势导出的场相同，但与由Jefimenko公式导出的场不同。本文指出了在杰菲缅科方程的推导过程中，关于部分空间和时间导数的一个数学错误。
Instantaneous fields in classical electrodynamics
本文用伽利略不变电磁场的瞬时场来表示麦克斯韦理论中的延迟场，并求出一个矢量函数，它的空间和时间导数将瞬时场变换为延迟场。我们的结论是，瞬时场可以作为非物理对象形式上引入经典电动力学，从而可以用来寻找物理延迟场。
Forces between electric charges in motion: Rutherford scattering, circular Keplerian orbits, action-at-a-distance and Newton's third law in relativistic classical electrodynamics
本文将经典电磁学中由延迟势导出的运动电荷间力的标准公式与最近发展起来的考虑瞬时电荷间力的相对论经典电动力学理论所得到的公式进行了比较。讨论的问题包括小角度卢瑟福散射、杰克逊最近的"扭矩悖论"和圆形开普勒轨道。与狭义相对论一致的结果只在瞬时相互作用下得到。本文论证了在经典电磁场和牛顿引力场中，带延迟场的稳定圆周运动是不可能的。
We derive the rate of emission of electromagnetic energy by an accelerating point charge, with the acceleration and velocity in the result being taken at the present time in the motion of the accelerating charge. This contrasts with the usual textbook derivation, which calculates the energy radiated through the surface of a large sphere, and gives the rate of radiated energy in terms of the acceleration and velocity at an arbitrary retarded time.
Light propagation is viewed as a process involving mutual creation of electric and magnetic fields. This viewpoint is used to argue that the conventional retarded solutions to electromagnetic wave equations (whose source is a current density in this work) are wrong, and to solve the wave equations in a different way by tracking every step in the said process. It turns out that the solutions to the wave equations, or the emitted fields from the current density, have equally weighted advanced and retarded components. After these components are explained for their mathematical and physical origin…
A Simple Derivation of Lorentz Self Force
通过对延迟场进行平均，导出了任意运动带电粒子的洛伦兹自作用力。推导是简单的，同时在教学上是可以理解的。得到了带电粒子沿圆锥曲线运动时的辐射反应。我们确定了质量重整化的基本概念。
Double (implicit and explicit) dependence of the electromagnetic field of an accelerated charge on time: Mathematical and physical analysis of the problem
我们考虑沿轴作匀速运动的电荷的电磁场。我们发现，如果只考虑滞后相互作用（即场对时间的纯隐式依赖），则由Liénard-Wiechert势得到的场不满足麦克斯韦方程组。我们证明了当且仅当同时考虑延迟相互作用和直接相互作用（所谓的“超距作用”）时，加速电荷产生的场满足麦克斯韦方程组。
Average Lorentz Self-Force From Electric Field Lines
本文利用库仑定律、电磁场的相对论变换和汤姆逊构造，将带电粒子作匀加速运动时电磁场的推导[1]推广到变加速度（分段常数）运动时的电磁场推导[2]。通过对延迟时间的场进行平均，导出了带电粒子作任意非相对论运动时的平均洛仑兹自作用力。
We calculate the electromagnetic self-force of a uniformly charged spherical ball moving on a rectilinear trajectory, neglecting the Lorentz contraction.
Derivation and physical interpretation of the general solutions to the wave equations for electromagnetic potentials
本文从推迟源密度推导电磁势的非齐次波动方程，在k空间求解得到无奇点的通解，并讨论其物理意义，可应用于凝聚态与荧光成像。
Electromagnetic energy, momentum and forces in a dielectric medium with losses
从电磁场的能量动量张量和机械能动量张量出发，得到了电磁力和机械力的能量守恒方程和平衡方程。得到了有损耗介质中亚伯拉罕力的方程
Compatibility of Larmor's formula with radiation reaction for a radiating charge
它表明，众所周知的差距在经典电动力学之间的功率损失计算的辐射反应，从拉莫尔公式，是简洁地理解时，一个适当的区别是表示在“实时”和那些表示在延迟时间方面的数量。它明确地表明，一个加速电荷，采取是一个球的消失小半径$r_{\rm o} $，经验在任何时候都是一个自作用力成正比的加速度，它在一个时间$r_{\rm o} /c$较早，而所做的工作的收费率是由一个标量产品的自作用力与瞬时（目前）的速度值。现在，如果加速度的延迟值用加速度的当前值来表示，那么我们就可以根据辐射反应方程得到所做的功的速率，然而，如果我们用速度的延迟值来表示速度的当前值，那么我们就可以得到熟悉的拉莫尔辐射公式。从这两个简单的关系，我们表明，他们不同，因为拉莫尔的公式，与辐射反应，不是写在规定的电荷运动的量的实时值，而是表示在时间延迟的值。此外，它明确表明，在这两个公式的辐射功率损耗的差异完全匹配的延迟和真实时间之间的自场的能量变化的时间速率的差异。由此可见，为了使两个公式相互符合，特别引入一个与加速度有关的能量项（在流行的文献中通常称为肖特项）是多余的。
Can Maxwell's equations be obtained from the continuity equation?
我们制定了一个存在定理，指出，给定本地化的标量和矢量的时间依赖源满足连续性方程，存在两个延迟场，满足一组四个场方程。如果将该定理应用于通常的电磁电荷和电流密度，则延迟场与电场和磁场等同，并且相关的场方程与麦克斯韦方程组等同。这个定理的应用表明，电荷守恒可以被认为是麦克斯韦方程组的基本假设。
An ab initio derivation of the electromagnetic fields of a point charge in arbitrary motion
从第一性原理出发，利用库仑定律和相对论变换，导出了加速电荷的电磁场。电场和磁场推导出的第一个瞬时静止帧的加速电荷，没有明确使用高斯定律，一种方法不同，在文献中。然后，我们计算了具有非相对论运动的加速电荷的电磁场。这些场的表达式，假定只精确到速度$β$的一阶，令人惊讶地产生了加速度场的所有项，只在速度场中缺少一个因子$1-β^2$。推导明确地显示了起源的字段表达式中的各种条款，当表示相对于时间延迟的位置的电荷。一个简单的变换从瞬时静止帧，使用相对论多普勒因子，产生表达式的电磁场的电荷以任意速度移动。场的表达式推导不使用Liénard-Wiechert势，从而避免了这些潜在的任何空间或时间的衍生物在延迟时间的评估。
We consider classical electromagnetic systems in which the current density ${\bf J}$ does not change with time, but has nonzero divergence, so that electric charge does build up steadily over time. We show that for such a system, the \emph{exact} electromagnetic fields are given by the Coulomb and Biot-Savart laws with the sources evaluated at the \emph{present} (rather than retarded) time, even though the charge density is changing over time.
We calculate the self-force of a point charge in rectilinear motion, using a local method and compare our results with those from the literature.
Comment on `Electromagnetic force on a moving dipole'
使用拉格朗日形式主义，由Kholmetskii，Missevitch和Yarman（2011，Eur. J. Phys. 32，873）被发现遗漏了一些重要的术语。
The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to the old problem of what the electromagnetic energy-momentum tensor is. Electromagnetic energies and forces will be examined thoroughly from a new point of view in the framework of Distribution Theory.
A new form of the energy-momentum tensor of the interaction of an electromagnetic field with a non-conducting medium. The wave equations. The electromagnetic forces
本文提出了一种新的方法，不用麦克斯韦方程组和坡印亭定理，直接求出介质中电磁场的能量动量张量。能量-动量张量具有新的性质和结果。它的线性不变量是电磁场的拉格朗日密度。从张量中得出能量密度的能量守恒方程、通量能量密度方程和这些能量值的波动方程。动量密度的波动方程描述了动量和角动量的同时传递，而与辐射偏振无关。从张量出发，导出了电磁力对动量密度的闵可夫斯基和亚伯拉罕形式的平衡方程，证明了它们的等价性和互补性。得到了Abraham力的表达式。证明了它的发散度等于零。导出了连续介质中电磁力的张量方程和平衡方程。
The symmetric tensor energy-impulse of interaction of collective of electric charges with an electromagnetic field is received. A system of covariant energy and momentum conservation equations or a system of equations for the collective motion of charged particles is derived from this tensor. From this system Expressions are derived for collective electrodynamics forces. From the energy-momentum tensor derived the tensor of collective electrodynamics forces is.
Classical formulations of the electromagnetic self-force of extended charged bodies
几个noncovariant制剂的电磁自作用力的扩展带电体，已开发的背景下的带电粒子的经典模型，进行了比较。各种不同的自作用力表达式的数学等价性明确证明了这些表达式直接从另一个。的自作用力配方和它们的意义在更广泛的背景下，经典带电粒子模型的适用性进行了讨论。
On retardation, radiation and Liénard-Wiechert type potentials in electrodynamics and elastodynamics
本文的目的是利用电动力学和弹性动力学理论研究非均匀运动点源引起的延迟和辐射的基本问题。本文研究和比较了延迟电磁场和延迟弹性动力场。对于一般点源的非匀速运动，导出了点电荷和点力的Liénard-Wiechert型势和辐射场与非辐射场。
Self Force of a Charge in a Real Current Environment
对单个电荷的电磁辐射分析表明，辐射功率取决于电荷的延迟加速度。因此，为了保持一致性，一个不受外力影响的加速电荷应该逐渐失去它的加速度，直到它的总能量被辐射出去。计算表明，补偿辐射的电荷自身力与加速度的导数成正比。然而，当在电荷的运动方程中使用这种自作用力时，得到的解是发散的，此时加速度趋于无穷大。这意味着在单电荷问题的解中存在不一致性。然而，在守恒麦克斯韦电荷密度的构造中，在对应的世界线上隐含着一个积分，它对应于带电时空事件的集合。因此，人们可以一致地认为，"自作用力“是一个电荷由于另一个电荷在延迟位置上而受到的力。从这一观点看，能量是明显守恒的，辐射过程表现为对馈源的吸收阻力。本工作的目的是从实际电流的行为中了解单个电荷的行为，对应于在世界线上运动的电荷集a，并研究与连续电荷的辐射电阻相关联的电荷的自作用力的模拟。
The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centered on the charge's present position. The finite part of the self-force obtained is the well-established relativistic radiation reaction, while its divergent part implies the pre-relativistic longitudinal electromagnetic mass of Abraham.
The problem of defining work done on electromagnetic field (EMF) via moving charges does not have a ready solution, because the standard Hamiltonian of EMF does not predict gauge-invariant energy changes. This limits applications of statistical mechanics to EMF. We obtained a new, explicitly gauge-invariant Hamiltonian for EMF that depends only on physical observables. This Hamiltonian allows to define thermodynamic work done on EMF and to formulate the second law for the considered situation. It also leads to a direct link between this law and the electrodynamic arrow of time, i.e. choosing r…
Electromagnetic Force and Momentum
这篇文章发表在Journal of Optics 19（2017）013001的“结构光路线图”第4部分。第4节描述了经典电磁力和动量理论的基本要素。
We obtain the fields and electromagnetic self-force of a charge distributed on the surface of a sphere undergoing rigid motion at constant proper acceleration, where the charge distribution has axial symmetry about the direction of motion. A closed-form expression for the self-force is given in terms of the multipole moments of the charge distribution. Applications to the electrodynamics of a dipole, and to electromagnetic self-force near a horizon (in spacetime) are discussed.
Electromagnetic force and torque are typically derived from a stress tensor in conjunction with Maxwell's equations of classical electrodynamics. In some instances, the Principle of Least Action (built around a Lagrangian) can be used to arrive at the same mathematical expressions of force and torque as those derived from a stress tensor. This paper describes some of the underlying arguments for the existence of a Lagrangian in the case of certain simple physical systems. While some formulations of electromagnetic force and torque admit a Lagrangian, there are other formulations for which a La…
The force exerted by an electromagnetic body on another body in relative motion, and its minimal expression, the force on moving charges or \emph{Lorentz' force} constitute the link between electromagnetism and mechanics. Expressions for the force were produced first by Maxwell and later by H. A. Lorentz, but their expressions disagree. The construction process was the result, in both cases, of analogies rooted in the idea of the ether. Yet, the expression of the force has remained despite its production context. We present a path to the electromagnetic force that starts from Ludwig Lorenz' re…
Electromagnetic force and torque in Lorentz and Einstein-Laub formulations
经典电动力学的洛伦兹力定律要求在电场作用于磁性材料的情况下引入隐藏的能量和隐藏的动量。与此相反，爱因斯坦-劳布公式并没有引用隐藏的实体。由电磁场施加在给定物体上的总的力和扭矩与力和扭矩密度是否使用洛伦兹定律或爱因斯坦和劳布定律来计算无关。除了隐藏的实体之外，这两种公式的不同之处仅在于它们在整个材料介质中的预测力和扭矩分布。
The origin of the Schott term in the electromagnetic self force of a classical point charge
Schott项是带电点粒子电磁自作用力的三阶项。自作用力可以通过在围绕一段世界线的窄超管的侧面上积分电磁应力-能量-动量张量来获得。这个计算已经使用两个不同的超管（称为狄拉克管和巴巴管）重复了很多次，然而在以前使用巴巴管的计算中，肖特项并没有因为这个积分而出现。为了恢复Lorentz-Abraham-Dirac方程，许多作者在非电磁场对总动量的贡献中加入了一个特别的补偿项。本文用电磁应力-能量-动量张量直接积分的方法得到了Schott项。
Electromagnetic energy-momentum and forces in matter
讨论了电磁场在物质介质中的能量动量分布和电磁场的机械力。对这些概念存在着长期的争论。闵可夫斯基和亚伯拉罕能量动量张量是最著名的。我们提出了一个解决这个问题，这似乎是自然的和自洽的从理论和实验的角度来看。
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