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Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an…
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…
The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a…
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…
We formulate a theory of classical electrodynamics where the only admissible electric charges are topological singularities in the electromagnetic field, and charge quantization is accounted by the Chern theorem, such that Dirac magnetic…
A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…
In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalized continuum theory possesses a weak…
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical…
In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields, in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the…
Lagrange scalar densities which are concomitants of two scalar fields, a pseudo-Riemannian metric tensor, and their derivatives of arbitrary differential order are investigated in a space of four-dimensions. I construct the most general…
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii {\it et al} showed that the resulting evolution contains a…
A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is…
A relativistic version of the correspondence principle, a limit in which classical electrodynamics may be derived from QED, has never been clear, especially when including gravitational mass. Here we introduce a novel classical field theory…
Although the expressions for energy densities involving electric and magnetic fields are exactly analogous, the connections to forces and electromagnetic potentials are vastly different. For electrostatic situations, the changes in the…
We provide a full realization of the electromagnetic duality at the boundary by extending the phase space of Maxwell's theory through the introduction of edge modes and their conjugate momenta. We show how such extension, which follows from…
This communication is devoted to a brief historical framework and to a comprehensive critical discussion concerning foundational issues of Electrodynamics. Attention is especially focused on the events which, about the end of XIX century,…
It is considered a mechanism of dynamical symmetry breaking for extended Ue(1)xUg(1) containing, one vector gauge field 'A' (photon) and one pseudo-vector gauge field 'C' (pseudo-photon). By choosing a particular solution of the equations…
Due to the nonlinearity of QED, a static charge becomes a magnetic dipole if placed in a magnetic field. Already without external field, the cubic Maxwell equation for the field of a point charge has a soliton solution with a finite field…