Related papers: Direct, analytic solution for the electromagnetic …
Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
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…
In the classical electrodynamics, different gauges, i.e. connections between the electromagnetic potentials, are used. Some of these are quite specific and intended for calculations in special systems (absence of free charges, etc.). All of…
We investigate the space-time dependence of electromagnetic fields produced by charged participants in an expanding fluid. To address this problem, we need to solve the Maxwell's equations coupled to the hydrodynamics conservation equation,…
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
We investigate the effective potential for Abelian Maxwell--Chern--Simons systems. The calculations follow an alternate approach, recently proposed as a gauge invariant formulation of the effective potential, constructed in terms of a gauge…
We present solutions to the classical Liouville equation for ergodic and completely integrable systems - systems that are known to attain equilibrium. Ergodic systems are known to thermal equilibrate with a Maxwell-Boltzmann distribution…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
In this comment it is argued that the argument for a unique determination of the electromagnetic potentials in classical electrodynamics in [1] is flawed. To the contrary the "gauge freedom" of the electromagnetic potentials has proven as…
The proper time formalism for a particle propagator in an external electromagnetic field is combined with the path-dependent formulation of the gauge theory to simplify the quasiclassical propagator. The latter is achieved due to a specific…
It is known that with restrictions on the type of the constitutive equations, Maxwell's equations in non-uniform media can sometimes be reduced to two 2nd order differential equations for 2 scalar quantities only. These results have…
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
We present a new class of exact nonsingular solutions for the Maxwell equations in vacuum, which describe the electromagnetic field of the counterpropagating focused laser beams and the subperiod focused laser pulse. These solutions are…
We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an…
Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating…