Related papers: On a quaternionic Maxwell equation for the time-de…
We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is…
This paper deals with classical solutions of the modified chiral model on $R^{2+1}$. Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of…
This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the…
On the basis of a non-local Lagrangian for Maxwell equations in a dispersive medium, the energy-momentum tensor of the field is derived. We obtain the Field equations through variational methods and an extension of Noether theorem for a…
Using an explicit Euler substitution it was obtained a system of differential equations, which can be used to find the solution of time-dependent 1-dimentional Schr\H{o}dinger equation for a general form of the time-dependent potential.
In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…
In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant…
We study radiation by a fast particle in a medium with a finite chiral chemical potential. The medium's anomalous response encompasses the chiral magnetic effect, enabling novel chiral Cherenkov and pair production processes. The kinematics…
In this work we propose a biquaternionic reformulation of a fractional monochromatic Maxwell system. Additionally, some examples are given to illustrate how the quaternionic fractional approach emerges in linear hydrodynamic and elasticity.
In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
Ermakov has shown how the solution to the classical harmonic oscillator in one spatial dimension with general time-dependent frequency can be reduced to the time-independent case and an associated nonlinear ordinary differential equation,…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
The response of chiral fermions to time and space dependent axial imbalance & constant magnetic field is analyzed. The axialvector-vector-vector (AVV) three-point function is studied using a real-time approach at finite temperature in the…
The search for time-harmonic solutions of nonlinear Maxwell equations in the absence of charges and currents leads to the elliptic equation $$\nabla\times\left(\mu(x)^{-1} \nabla\times u\right) - \omega^2\varepsilon(x)u = f(x,u)$$ for the…
In this paper, we consider the Maxwell-Klein-Gordon and Maxwell-Chern-Simons-Higgs systems in the temporal gauge. By using the fact that when the spatial gauge potentials are in the Coulomb gauge, their $\dot{H}^1$ norms can be controlled…
For explicitly time depending mass density, which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approximation or related…
The concept of electromagnetic field can be neatly formulated by recognizing that the simplest form of the four-force is indeed feasible. We show that Maxwell's equations almost entirely stem from the properties of spacetime, notably from…