Related papers: Generalized Hertz vector in the dissipative electr…
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…
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…
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when…
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…
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…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory proposed in Ref. [Lazo et al, Phys. Rev. D…
Electric vector potential $\Theta(\boldsymbol{r})$ is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential $\Phi(\boldsymbol{r})$…
We consider electromagnetic radiation of a charged particle bunch moving uniformly along a corrugated planar metallic surface. It is assumed that the wavelengths under consideration are much larger than the period and the depth of…
The article presents an alternative approach to the definition of vector electrodynamic potential and its properties. It is shown that generally it has vortical and potential components. The system of differential equations of generalized…
We give an integral expression for the vector potential of a time-independent, steady azimuthal current density. Our derivation is substantially simpler and somewhat more general than others given in the literature. As an illustration, we…
We introduce the generalized Lorentz gauge condition in the theory of quantum electrodynamics into the general vector-tensor theories of gravity. Then we explore the cosmic evolution and the static, spherically symmetric solution of the…
This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular,…
We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is…
We review two procedures for constructing the vector potential of the electromagnetic field on Kerr spacetime, namely, the classic method of Cohen & Kegeles, yielding $A^\mu$ in a radiation gauge, and the newer method of Frolov et al.,…
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…
The analysis of vector fields is crucial for the understanding of several physical phenomena, such as natural events (e.g., analysis of waves), diffusive processes, electric and electromagnetic fields. While previous work has been focused…
We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge…
Smooth vector fields on $\mathbb{R}^n$ can be decomposed into the sum of a gradient vector field and divergence-free (solenoidal) vector field under suitable hypotheses. This is called the Helmholtz-Hodge decomposition (HHD), which has been…
We are calculated the expectation value of the axial-vector current induced by the vacuum polarization effect of the Dirac field in constant external electromagnetic field. In calculations we use Schwinger's proper time method. The…