The Lorentz Condition is Equivalent to Maxwell Equations
Edmund A. Di Marzio
证明了电磁四维矢量密度A的守恒定律--洛仑兹条件和洛伦兹变换合起来等价于微观麦克斯韦方程组。
It is shown that the Lorentz condition which is a conservation law on the electromagnetic four-vector-density A, plus the Lorentz transformation, taken together, are equivalent to the microscopic Maxwell's equations.
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Some Variations on Maxwell's Equations
在这篇文章的第一部分，我们讨论了两个变化的麦克斯韦方程组，已在早期的工作-一类非线性麦克斯韦理论与明确的伽利略限制（和相应的广义杨米尔斯方程），和线性修改的动机耦合的电磁势与一定的非线性薛定谔方程。在最后一节中，我们将重温洛伦兹的一个旧思想，写出麦克斯韦方程组，以证明这样一种理论：同性电荷之间的排斥静电力与异性电荷之间的吸引静电力的大小根本不同。我们详细阐述了洛伦兹的描述，通过电和磁场强度，其控制方程分为两个完全相对论性的麦克斯韦系统-一个描述普通的电磁，和其他描述一个普遍的吸引力或排斥力的长程力。如果这样的力不能被已知的物理原理{ \it a priori}排除，那么它的大小应该通过实验来确定或界定。如果它真的存在，那么有趣的可能性就超出了洛伦兹早期关于它与（牛顿）引力的关系的猜想。
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding generalization of the Lorentz force is established for the considered model. On a stationary background, we have found the integral of motion of the energy type. This integral is used to resolve the radial dynamics of test particles in a spherically symmetric electrostatic background.
We show that if we start with the free Dirac Lagrangian, and demand local phase invariance, assuming the total phase coming from two independent contributions associated with the charge and mass degrees of freedom of charged Dirac particles, then we are forced to introduce two massless independent vector fields for charged Dirac particles that generate all of electrodynamics and gravitodynamics of Heaviside's Gravity of 1893 or Maxwellian Gravity and specify the charge and mass currents produced by charged Dirac particles. From this approach we found: (1) a new set of Maxwell-Lorentz equations…
The exact proof that Maxwell equations with the 3D E and B are not Lorentz covariant equations. The new Lorentz invariant field equations
本文从几何代数和张量形式两个方面严格证明了通常的三维电场矢量E{bold}和三维磁场矢量B{bold}的麦克斯韦方程组不是洛伦兹协变方程组。因此，它们不等价于具有观察者独立量的场方程，电磁场张量Fsup{ab}（张量形式主义）或具有双向量场F（几何代数形式主义）。不同的4D代数对象被用来表示标准的观察者依赖和新的观察者独立的电场和磁场。标准电磁学和狭义相对论之间根本不一致的证明并不依赖于用来表示电场和磁场的四维代数对象的特征。用1-向量E和B，双向量Esub{HL}和Bsub{HL}以及抽象张量4-向量Esup{a}和Bsup{a}建立了Lorentz不变场方程。所有这些量都是在没有参考系的情况下定义的。这样的场方程与实验完全一致。
We discuss the modified Maxwell action of a $K_{F}$-type Lorentz symmetry breaking theory and present a solution of Maxwell equations derived in the cases of linear and elliptically polarized electromagnetic waves in the vacuum of CPT-even Lorentz violation. We show in this case the Lorentz violation has the effect of changing the amplitude of one component of the magnetic field, while leaving the electric field unchanged, leading to non-orthogonal propagation of eletromagnetic fields and dependence of the eccentricity on $κ$-term. Further, we exhibit numerically the consequences of this effec…
The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations
本文用几何代数和张量形式研究了通常的麦克斯韦方程组（ME）分别与三维电场和磁场矢量E和B的洛伦兹变换（LT）和标准变换（ST）。不同的4D代数对象被用来表示通常的观察者相关和新的观察者独立的电场和磁场。发现ME的ST不同于它们的LT，因此具有3D E和B的ME在LT上不是协变的，而是在ST上。所获得的结果不依赖于用于表示电场和磁场的4D代数对象的特征。用1-向量E和B、双向量E_{Hv}和B_{Hv}以及抽象张量4-向量E^{a}和B^{a}给出洛伦兹不变场方程。所有这些量都是在没有参考系的情况下定义的，即，绝对数量。当引入一些基时，它们被表示为包括分量和基的基于坐标的几何量。它明确表明，这种几何方法与实验，例如，法拉第盘，在所有相对运动的惯性参考系中，这不是用3D E和B及其ST的通常方法的情况。
Here we discuss the presence of CPT-even Lorentz violation (LV) in the presence of a deformed Heisenberg algebra that leads to a minimum length (ML). We consider the case of a Maxwell lagrangian modified by the presence of a $K_{F}$ CPT-even LV theory and ML. We then derive a set of modified Maxwell equations in the cases of LV and ML and only ML. We verified that in the case of electromagnetic waves in the vacuum the presence of ML does not change the consequences of LV. On the other hand, in a material media ML changes the whole set of equations that can lead to important effects with respec…
From the Field Electron Model to the Unified Field Theory
统一场是麦克斯韦-洛伦兹场。严格满足标准四维形式的Maxwell-Lorentz方程。这是通过涉及新的基本场源来实现的，严格定义需要更高的维度。源电流彼此不能充分“看到”，以至于在空间的任何方向上的每个点上，都有两个具有不同电荷符号的电流。每个这样的带电源在麦克斯韦-洛仑兹场中按照运动定律运动，并且它们中的每一个都独立于其他带电源，根据麦克斯韦-洛仑兹方程产生场。运动定律可以从具有“必要”性质的稳定的全同电子形式的溶液存在的条件中找到。要发现的运动规律是由电子产生的条件严格限定的！如果电子存在，那就意味着质子、原子和宇宙也存在。所有的粒子和场--它们只是麦克斯韦-洛伦兹场与其源之间相互作用的可见展示！
Comment on ``Do Zero-energy Solutions of Maxwell Equations Have the Physical Origin Suggested by A. E. Chubykalo?" by V.V. Dvoeglazov
这是对萨卡特卡斯研讨会论文集“洛伦兹群、CPT和中微子”（世界科学，新加坡，2000年）中提出的反对意见的回答。335-341.
The consequences of complex Lorentz force and violation of Lorenz gauge condition
引入复洛伦兹力，并将其推广到磁标量。这个标量被发现是与一个占主导地位的磁场渗透整个空间。在洛仑兹复力中引入了一个附加力。磁标量与真空能量有关。从扩展的电流密度变换导出了Proca-Maxwell的大质量电动力学。Proca-Maxwell理论在扩展的规范变换（电流-电荷密度）下是不变的。洛伦兹规范条件表示光子电荷守恒。任何违反洛伦兹规范（光子电荷）或电子电荷守恒的行为都会导致自旋为零的标量粒子。这表现在超导性上。包含电子和光子的总电荷总是守恒的。由于超导性，光子电荷与电子电荷通过$e_p=\sqrt{\frac{m_p}{m_e}}\,\,e$相关。超导体中的光子被证明是巨大的。指出用复数形式表示的麦克斯韦方程组更便于研究对偶变换。
On non-equivalence of Lorentz and Coulomb gauges within classical electrodynamics
它表明，众所周知的程序证明等价的电场计算使用洛伦兹和库仑规范的表达式是不正确的。这两种规范之间的差异是由于标量位扰动传播速度的差异。作为一个辅助结果，它证明了电场的解决方案不能直接从麦克斯韦方程组，即不引入标量和矢量势。
Adopting Schwinger's formalism for inferring Maxwell-Lorentz equations (MLEs) and combining three ingredients: (i) the laws of gravitostatics, (ii) the Galileo-Newton principle of relativity and (iii) existence of gravitational waves which travel in vacuum with a finite speed $c_g$, we inferred two sets of gravito-Maxwell-Lorentz Equations (g-MLEs). One of these sets corresponds to Heaviside's Gravity of 1893 and the other set corresponds to what we call Maxwellian Gravity (MG). HG and MG are mere two mathematical representations of a single physical theory called Heaviside-Maxwellian Gravity …
Adopting two independent approaches (a) Lorentz-invariance of physical laws and (b) local phase invariance of quantum field theory applied to the Dirac Lagrangian for massive electrically neutral Dirac particles, we rediscovered the fundamental field equations of Heaviside Gravity (HG) of 1893 and Maxwellian Gravity (MG), which look different from each other due to a sign difference in some terms of their respective field equations. However, they are shown to represent two mathematical representations of a single physical theory of vector gravity that we name here as Heaviside-Maxwellian Gravi…
In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed obtained. We then find with these generalized coordinate transformations acting on Maxwell's equations that the electromagnetic field transformations are nevertheless unchanged. We find further, that if we assume the absence of magnetic monopoles, in accordance with Maxwell's theory, our generalized transformations are then restricted to be the conventional ones. …
The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor.
We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event $x^μ(τ)$. By admitting unconstrained commutation relations between the positions and velocities, the associated electromagnetic gauge fields are in general dependent on the parameter $τ$, which plays the role of time in Newtonian mechanics. Standard Maxwell theory emerges from this system as a $τ$-independent equilibrium limit. In this paper,…
It is well known that the field equations of teleparallel theory which is equivalent to general relativity (TEGR) completely agree with the field equation of general relativity (GR). However, TEGR has six extra degrees of freedom which spoil the true physics. These extra degrees are related to the local Lorentz transformation. In this study, we give three different tetrads of flat horizon space-time that depend only on the radial coordinate. One of these tetrads contains an arbitrary function which comes from local Lorentz transformation. We show by explicate calculations that this arbitrary f…
Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
洛伦兹力定律是经典电动力学的第五大支柱，其他四个是麦克斯韦的宏观方程。洛仑兹定律是电磁场作用于包含电荷和电流分布的体积上的力的普遍表达。如果电偶极子和磁偶极子也碰巧存在于材料介质中，则传统上通过用束缚电荷和束缚电流密度表示相应的极化和磁化分布来处理它们，随后分别将其添加到自由电荷和自由电流密度。通过这种方式，麦克斯韦的宏观方程被简化为他的微观方程，洛伦兹定律有望提供物质体在空间和时间所有点上电磁力密度的精确表达。本文提出了洛伦兹定律与狭义相对论基本原理不相容的无可争议的理论证据。我们认为，必须放弃洛伦兹定律，而采用一个更一般的电磁力密度表达式，如A。1908年，爱因斯坦和J. Laub。爱因斯坦-劳布公式不仅与狭义相对论一致，还解决了经典电动力学中长期存在的“隐藏动量”问题。
The development of relational electromagnetism after Gauss appears to stop around 1870. Maxwell recognised relational electromagnetism as mathematically equivalent to his own formulae and called for an explanation of why so different conceptions have such a large part in common. We reconstruct relational electromagnetism guided by the No Arbitrariness Principle. Lorenz' idea of electromagnetic waves, together with the "least action principle" proposed by Lorentz are enough to derive Maxwell's equations, the continuity equation and the Lorentz' force. We show that there must be two more symmetr…
It has been said that Maxwell's theory of electromagnetic field is relativistic as Einstein showed that these axioms of Maxwell are all Lorentz invariant. We investigate some issues regarding these results.
Unification of Gravity with Electromagnetism
麦克斯韦、洛伦兹、米尔恩、狄拉克和费曼的原理结合起来，统一了引力和电磁学。
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