Related papers: A derivation of Maxwell's equations using the Heav…
We reformulate classical electromagnetism as the statistical mechanics of lines of electric flux with dynamics described by the string action in four dimensions. The retarded solution to Maxwell's equations emerges naturally as an average…
Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic…
Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency…
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
A mathematical proof is given that Maxwell's equations are an {\it artifact} of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms,…
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
In Maxwell's equations, the electric field can be expressed as the sum of the Coulombic field associated with the electric charge and the induced field associated with the time variation of the magnetic field from Faraday's law. The same…
The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum field theory approach. The electron inertia problem is analyzed within the…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
We show that the linearized equations of the incompressible elastic medium admit a `Maxwell form' in which the shear component of the stress vector plays the role of the electric field, and the vorticity plays the role of the magnetic…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…