Related papers: Electromagnetic source transformations and scalari…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
We present a unified framework that fully represents electromagnetic potentials, fields, and sources in vacuum, based on a reinterpretation of the classical Hertz-potential formalism. In this construction, $\phi$, $A$, $E$, $B$, $\rho$, and…
Electric and magnetic Hertz potentials are a formalism for obtaining solutions of Maxwell's equations from solutions of the inhomogeneous wave equation, with polarisation and magnetisation as the sources. We provide an overview of their…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
In this work, we focus on the theory of Gravito-Electromagnetism (GEM) -- the theory that describes the dynamics of the gravitational field in terms of quantities met in Electromagnetism -- and we propose two novel forms of metric…
Potential-based formulation with generalized Lorenz gauge can be used in the quantization of electromagnetic fields in inhomogeneous media. However, one often faces the redundancy of modes when finding eigenmodes from potential-based…
The time-dependent, geometric method for high-energy limits and inverse scattering is applied to nonrelativistic quantum particles in external electromagnetic fields. Both the Schr"odinger- and the Pauli equations in R^2 and R^3 are…
We identify a set of Hertz potentials for solutions to the vector wave equation on black hole spacetimes. The Hertz potentials yield Lorenz gauge electromagnetic vector potentials that represent physical solutions to the Maxwell equations,…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
The reduction of the three-dimensional classical electromagnetism is performed in a twofold way. In the first case the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing…
The inhomogeneous wave equations for the scalar, vector, and Hertz potentials are derived starting from retarded charge, current, and polarization densities and then solved in the reciprocal (or k-) space to obtain general solutions, which…
Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The…
A new gauge-free electromagnetic gyrokinetic theory is developed, in which the gyrocenter equations of motion and the gyrocenter phase-space transformation are expressed in terms of the perturbed electromagnetic fields, instead of the usual…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
By modeling a dielectric medium with two independent reservoirs, i.e., electric and magnetic reservoirs, the electromagnetic field is quantized in a linear dielectric medium consistently. A Hamiltonian is proposed from which using the…
In the first part of the present work, we focus on the theory of gravitoelectromagnetism (GEM), and we derive the full set of equations and constraints that the GEM scalar and vector potentials ought to satisfy. We discuss important aspects…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…
This paper extends approach of our joint paper with K\"{a}hler and recent paper of the author, published in 2021, on problems of the static Maxwell system in three dimensional inhomogeneous media. Applied pseudoanalytic function theory…