The energy conservation law in classical electrodynamics
E. G. Bessonov
在经典Maxwell-Lorentz电动力学的框架下，重新考虑了能量守恒定律。
In the framework of the classical Maxwell-Lorentz electrodynamics the energy conservation law is reconsidered.
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The energy conservation law in classical electrodynamics 2
分析了在推导能量守恒定律时常见的逻辑错误，并提出了避免错误的方法。
It is shown that the well-known disparity in classical electrodynamics between the power radiated in electromagnetic fields and the power-loss, as calculated from the radiation reaction on a charge undergoing a non-uniform motion, is successfully resolved when a proper distinction is made between quantities expressed in terms of a "real time" and those expressed in terms of a retarded time. It is shown that the expression for the real-time radiative power loss from a charged particle is somewhat different from the familiar Larmor's formula, or in a relativistic case, from Liénard's formula.
Time symmetric electrodynamics, electric charge conservation, and the Lorenz gauge
该研究借助时间对称电动力学及 Frenkel、Wheeler 的早期观察，在带电点粒子可产生与湮灭的设定下，证明 Lorenz 规范条件与电荷守恒可由 Minkowski 空间中同一条“Wheeler 电子”闭合路径积分表达。
Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields. However, physical conservation principles come from symmetries such as those following from Noether's theorem, and these require potentials for their statement. Examples are given of potentials that describe fields correctly but that violate conservation principles, demonstrating that the correct sta…
It is customary to assume that the law of conservation of the angular momentum is violated for an asymmetric energy-momentum tensors. This is the reason for criticizing the Minkowski tensor and other asymmetric energy-momentum tensors. In this paper, it is shown that the laws of conservation of energy and momentum following from an asymmetric tensor in the form of its total divergence are equivalent to the divergence of its symmetric part. It is shown that the total divergence of the antisymmetric part of the asymmetric tensor is identically zero. From this, it follows that for the asymmetric …
To Foundations of Classical Electrodynamics
本文讨论了经典电动力学中能量守恒定律的基础和粒子的引入。我们注意到一个逻辑错误，它发生在解释波印廷定理作为能量守恒定律。结果表明，电磁场与带电粒子系统的能量守恒和动量守恒定律不符合电动力学方程，而这些定律的违背表现在粒子的能量变化上。特别的例子被认为是有可能限制一种可能的领域的非电磁起源。我们希望，这项工作将允许产生一个更全面的分析，并刺激下一步的发展基础的经典和量子电动力学。
We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersion-negligible dielectric of refractive index $n$ and examine the consequences of the effective speed of light in a stationary dielectric, $c/n$, for D'Alembert's principle and the Lagrange equations. The principles of dynamics in the dielectric-filled space are then applied to the electromagnetic Lagrangian and we derive equations of motion for the macroscopic fields. A direct derivation of the total energy--momentum tensor from the field strength tensor for the electromagnetic field in a dielectric is used …
Conservation Laws in Generalized Riemann-Silberstein Electrodynamics
从用Riemann-Silberstein矢量表示的正、负螺旋度麦克斯韦方程组出发，导出了10个常用的和10个附加的庞加莱{é}不变量，后者与电磁自旋有关，即：电磁场的固有旋转或极化状态。这些不变量中的一些显然没有在以前的文献中讨论过。
Axiomatics of classical electrodynamics and its relation to gauge field theory
我们给出了一个简洁的公理介绍到经典电动力学的基本结构：它是基于电荷守恒，洛伦兹力，磁通量守恒，并存在本地和线性本构关系。用$D^i$和$H_i$表示的{ \it非齐次}麦克斯韦方程组是电荷守恒的结果，而用$E_i$和$B^i$表示的{ \it齐次}麦克斯韦方程组是从磁通量守恒和狭义相对论理论导出的。激发$D^i$和$H_i$通过本构关系与场强$E_i$和$B^i$相关联。最后，我们指出了这种公理化方法与规范场理论框架的关系。
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.
A gentle introduction to the foundations of classical electrodynamics: The meaning of the excitations (D,H) and the field strengths (E, B)
概述了电磁理论的公理结构。我们将把经典电动力学建立在（1）电荷守恒、（2）洛伦兹力、（3）磁通量守恒和（4）麦克斯韦-洛仑兹时空关系的基础上。这就产生了麦克斯韦方程组。除其他外，还将得出电场和磁场的解释和尺寸的结果。
We examine physical aspects for the electric version of a recently proposed logarithmic electrodynamics, for which the electric field of a point-like charge is finite at the origin. It is shown that this electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field. Afterwards we compute the lowest-order modification to the interaction energy by means of the gauge-invariant but path-dependent variables formalism. These are shown to result in a long-range ($1/r^3$-type) correction, in addition to a linear and another logarithmic correction, to the Coulo…
Flaws and ambiguities are pointed out upon examining the comment attempting to solve a problem as raised recently --- the currently accepted formulation of electromagnetic radiation of an accelerated charge violates the principle of conservation of energy. This problem is not solved by the comment, due to a misunderstanding in the meaning of the total radiated power crossing a sphere. An experiment is suggested to determine whether on not the currently accepted formulation is valid.
Remarks on classical pseudo-electrodynamics
本文研究了伪电动力学中的守恒定律与辐射场，通过无穷小变换下的作用量对称性推导出相关张量，分析了1+2维电偶极子辐射，并提出引入磁单极子的方法。
A self-action problem for a point-like charged particle arbitrarily moving in flat space-time of six dimensions is considered. A consistent regularization procedure is proposed which relies on energy-momentum and angular momentum balance equations. Structure of the angular momentum tensor carried by the retarded "Liénard-Wiechert" field testifies that a point-like source in six dimensions possesses an internal angular momentum. Its magnitude is proportional to the square of acceleration. It is the so-called {\em rigid} relativistic particle; its motion is determinated by the higher-derivative …
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as expected on physical grounds. The relativistic generalization is also presented.
We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b) Lorentz- and reparameterization-invariance, c) local conservation of energy and momentum. Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor. Its conservation requires the particles to obey standard Lorentz equa…
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb's law and Debye's screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type.
In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot get by without attributing energy to the elect…
Gauge Theory for the Rate Equations: Electrodynamics on a Network
耦合速率方程组在许多科学领域中无处不在，例如在量子点和分子的电子输运描述中。它们可以被理解为一个表达概率守恒的连续性方程。它表明，这个守恒定律可以通过构建一个类似于经典电动力学的规范理论的速率方程描述的可能状态的网络来实现。分析了这种规范理论的性质。事实证明，即使允许的跃迁形成稀疏网络，网络也是相对于电磁场最大连接的。发现电场和磁场的自由度相等。这些结果揭示了经典阿贝尔规范理论的结构，而不仅仅是速率方程的特殊动机。
We treat continuum electrodynamics as an axiomatic formal theory based on the macroscopic Maxwell--Minkowski equations applied to a thermodynamically closed system consisting of an antireflection-coated block of a simple linear dielectric material situated in free-space that is illuminated by a quasimonochromatic field. We prove that valid theorems of the formal theory of Maxwellian continuum electrodynamics are inconsistent with conservation laws for the inviscid incoherent flow of non-interacting particles (photons) in the continuum limit (light field) in the absence of external forces, pres…
Energy-momentum conservation of classical axion-electrodynamics is carefully analyzed in the Hamiltonian formulation of the theory. The term responsible for the energy transfer between the electromagnetic and the axion sectors is identified. As a special application the axion-to-light Primakoff-process in the background of a static magnetic field is worked out and the radiative self-damping of the axion oscillations is characterized quantitatively. The damping time turns out comparable to the age of the Universe in the preferred axion mass range.
Classical Electrodynamics: A Tutorial on its Foundations
我们将展示经典电动力学的基本结构。从（1）电荷守恒、（2）存在洛伦兹力密度和（3）磁通量守恒的公理出发，我们将导出麦克斯韦方程组。它们用场强$(E,{\cal B})$、激励$({\cal D},H)$和源$(ρ,j)$表示。这一基本的四个微物理方程组必须补充有点不太一般的本构假设，以使其成为一个完全确定的系统与适定的初始值问题。只有在这个阶段，才需要时空的距离概念（度量）。我们将讨论一组可能的本构假设，即${\cal D}\sim E$和$H\sim {\cal B}$。{ \em文件erik8a.tex，1999-07-27}
De Broglie wave, spontaneous emission and Planck's radiation law according to stochastic electrodynamics
关于普朗克黑体辐射定律的量子性质的想法在大多数物理学家的头脑中根深蒂固。爱因斯坦的工作，其中自发和诱导发射系数的引入，一直被认为是一个证明，量子能量离散性的原子在推导这一法律起着至关重要的作用。在我们的论文中，我们避免了这种观点。可以看出，分配给每个物质粒子的德布罗意波是粒子与电磁场零点振动相互作用的结果。谐振子的能量谱是从经典物理中的这一事实得到的，这与量子结果一致。从而解释了具有经典电磁零点辐射的经典电动力学--随机电动力学（SED）中能量离散性的产生。其次，我们从系统自洽的观点重新考虑了爱因斯坦的工作，并导出了普朗克公式。
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