Relativistic derivation of Maxwell's equations in vacuum and the axiomatic foundation of electrodynamics

A derivation of Maxwell's equations in vacuum for the curls of the electric and magnetic fields is given in which the starting point is the Lorentz transformation and the equations for the divergences of the fields. The derivation is used to construct a new axiomatic foundation of electrodynamics, in which the Lorentz force and the equations for the divergences of the fields are postulated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 66–71, December, 1983.     

Another Proof of the Equivalence Between the Duality Symmetric and Maxwell's Action

We show that the duality symmetric action is equivalent to the Maxwell's action at the quantum level by means of the Dirac's method, and find out that the set of Dirac's brackets on the full phase space is invariant under the dual transformation.     

Massive Electrodynamics and Magnetic Monopoles

Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass, electric, and magnetic currents (Dirac's monopole) coexist within this theory. Assuming that the space-time is torsionless, taking the photon mass zero, and turning to the Einstein gauge we obtain Maxwell's electrodynamics.     

On generalized electromagnetism and Dirac algebra

Using a framework of Dirac algebra, the Clifford algebra appropriate for Minkowski space-time, the formulation of classical electromagnetism including both electric and magnetic charge is explored. Employing the two-potential approach of Cabibbo and Ferrari, a Lagrangian is obtained that is dyality invariant and from which it is possible to derive by Hamilton's principle both the symmetrized Maxwell's equations and the equations of motion for both electrically and magnetically charged particles. This latter result is achieved by defining the variation of the action associated with the cross terms of the interaction Lagrangian in terms of a surface integral. The surface integral has an equivalent path-integral form, showing that the contribution of the cross terms is local in nature. The form of these cross terms derives in a natural way from a Dirac algebraic formulation, and, in fact, the use of the geometric product of Dirac algebra is an essential aspect of this derivation. No kinematic restrictions are associated with the derivation, and no relationship between magnetic and electric charge evolves from the (classical) formulation. However, it is indicated that in bound states quantum mechanical considerations will lead to a version of Dirac's quantization condition. A discussion of parity violation of the generalized electromagnetic theory is given, and a new approach to the incorporation of this violation into the formalism is suggested. Possibilities for extensions are mentioned.Work supported by the Department of Energy, contract DE-AC03-76SF00515.     

A relationship between the Dirac and Maxwell equations

It is shown that an analogue of Dirac's equation may be constructed from Milner's extension of Maxwell's equations and a comparison of the algebraic and physical features of the equations made.     

Conformal invariance of Maxwell's equations with magnetic charges

It is shown that Maxwell's equations when there exist isolated magnetic charges are invariant under conformal transformations.     

Field theory onR×S 3 topology. IV: Electrodynamics of magnetic moments

The equations of electrodynamics for the interactions between magnetic moments are written on R×S³ topology rather than on Minkowskian space-time manifold of ordinary Maxwell's equations. The new field equations are an extension of the previously obtained Klein-Gordon-type, Schrödinger-type, Weyl-type, and Dirac-type equations. The concept of the magnetic moment in our case takes over that of the charge in ordinary electrodynamics as the fundamental entity. The new equations have R×S³ invariance as compared to the Lorentz invariance of Maxwell's equations. The solutions of the new field equations are given. In this theory the divergence of the electric field vanishes whereas that of the magnetic field does not.Research supported in part by the Colgate Research Council and by the Center for Theoretical Physics, University of Maryland.     

On the “Equivalence” of the Maxwell and Dirac Equations

It is shown that Maxwell's equation cannot be put into a spinor form that is equivalent to Dirac's equation. First of all, the spinor in the representation of the electromagnetic field bivector depends on only three independent complex components whereas the Dirac spinor depends on four. Second, Dirac's equation implies a complex structure specific to spin 1/2 particles that has no counterpart in Maxwell's equation. This complex structure makes fermions essentially different from bosons and therefore insures that there is no physically meaningful way to transform Maxwell's and Dirac's equations into each other.     

Charges and Fluxes in Maxwell Theory on Compact Manifolds with Boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincaré-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell’s equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.     

Derivation of quantum Maxwell equations from relativistic particle Hamiltonian

Given the Hamiltonian forN relativistic particles with charges and intrinsic magnetic moments interacting via pair potentials and self-interactions, we derive not only the particle equations, but also the full set of Maxwell's equations, thereby testing the consistency of particle equations, currents, and field equations in the Heisenberg picture.     

An electric charge system moving radially with the velocity of light

A solution is found for Maxwell's equations which are associated with a radial flow of electric charge moving with the speed of light.     

Variational principle for theP(4) affine theory of gravitation and electromagnetism

We propose a Lagrangian for theP(4) theory of gravitation and electromagnetism which is a straightforward generalization of the Einstein Lagrangian. A constrained Palatini variation of this Lagrangian yields the geometrical Einstein-Maxwell affine field equations. We show that these results can be extended easily to include both electric and magnetic charges. Finally, we consider conservation laws arising from the invariance properties of the Lagrangian.     

Two-potential theory of electric and magnetic charges via duality transformation

Dirac, Schwinger and Zwanziger theories of electric and magnetic charges are obtained via duality transformation. Analogous construction for three Euclidean dimensions, with magnetic charges interacting with electric currents, is also done. The role of Dirac strings as dislocations in the configurations of gauge potential is emphasized.     

磁电超材料折射率特性分析

基于麦克斯韦旋度方程, 将磁电超材料板中的电元件和磁元件分别等效为面电流和面磁流, 通过计算这些周期性面电流和面磁流在某个磁电超材料板上产生的总电场和总磁场, 获得了关于面磁流密度和面电流密度的两个方程, 进而推导出了周期性磁电超材料折射率与磁元件的磁导率、 电元件的介电常数和空间色散项之间关系的解析公式. 与传统的折射率计算公式不同, 该解析公式充分考虑到了空间色散以及磁电超材料的电元件和磁元件的相互作用. 折射率理论曲线和基于仿真实验数据的提取值曲线能很好地符合, 这说明文中推导的折射率公式能够正确地描述磁电超材料的负折射特性. 本文的结果将为分析电磁元件之间的相互作用以及设计负折射率符合一定要求的磁电超材料提供重要的理论参考. 关键词： 磁电超材料 周期性结构 负折射率     

Scaling gauge invariance and constancy of the speed of light

We prepose to extend Maxwell's equations of electromagnetism by treating the speed of light as a scalar function of space-time. This leads to scaling gauge invariance. As a consequence we find a conserved magnetic monopole current and nonconservation of electric charge.     

Extreme limit in linear polarisation ratio in step-index single- mode fibres with a central dip

From Maxwell's equations, using a Fourier expansion, spatial harmonic balance and Green's functions, closed-form expressions are found for the longitudinal electric and magnetic fields, for two orthogonally polarised modes of a birefringent fibre with or without a central index dip. Propagation constants can then be calculated to the desired degree of accuracy. Corrections up to third order are found to be significant. The linear polarisation ratio in the core and in the cladding is almost insensitive to birefringence but exhibits large variations in the central dip, where it deteriorates as the birefringence increases.     

关于真空中的位移电流、Maxwell方程组、电磁场的源及Jefimenko公式的几点注记

通过分析指出：电磁场是一个不可分割的整体，Maxwell方程组是电磁场的运动方程，电磁场的源是电荷与电流的分布，Jefimenko公式是真空中Maxwell方程组的解。     

Electromagnetic Coulomb gas with vector charges and “elastic” potentials: Renormalization group equations

We present a detailed derivation of the renormalization group equations for two-dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of “elastic” Coulomb gas. Such elastic Coulomb gases arise naturally in the study of the continuous melting transition of two-dimensional solids coupled to a substrate, either commensurate or with quenched disorder.     

Maxwell’s Equations as the One-Photon Quantum Equation

Maxwell's equations (the Faraday and Ampère-Maxwell laws) can be presented as a three-component equation in a way similar to the two-component neutrino equation. However, in this case, the electric and magnetic Gauss laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have also shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable and well understood quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum theories.     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.