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A new finite-range electromagnetic (EM) theory containing both electric and magnetic charges constructed using two vector potentials A^{} and Z^{} is formulated in the spacetime algebra (STA) and in the algebra of the three-dimensional…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
Within the framework of the universal algebra of the electromagnetic field, the impact of globally neutral configurations of external charges on the field is analyzed. External charges are not affected by the field, but they induce…
The influence of electric stochastic fields on the relativistic charged particles is investigated in the gauge invariant path integral formalism. Using the cumulant expansion one finds the exponential relaxation of the charge Green's…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
In this work, we present an explanation of the electric charge quantization based on a semi-classical model of electrostatic fields. We claim that in electrostatics, an electric charge must be equal to a rational multiple of the elementary…
We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then…
Integral relations and transformation rules are used to obtain, out of an asymptotic solution, a new group of four pairs of solutions to the double-confluent Heun equation. Each pair presents the same series coefficients but has solutions…
Many physically interesting quantities of the electromagnetic field can be computed using the electromagnetic scalar product. However, none of the existing expressions for such scalar product are directly applicable when the fields are only…
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…
The Euler-Heisenberg effective Lagrangian is used to obtain general expressions for electric and magnetic fields induced by non-linearity, to leading order in the non-linear expansion parameter, and for quasistatic situations. These…
The article focuses on the issue of the two definitions of charge, mainly the gauge charge and the effective charge of fundamental particles. Most textbooks on classical electromagnetism and quantum field theory only works with the gauge…
Using a gauge covariant operator technique we deduce the path integral for a charged particle in a stationary magnetic field, verifying the "midpoint rule" for the discrete form of the interaction term with the vector potential.
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
The quantum Gauss Law as an interacting field equation is a prominent feature of QED with eminent impact on its algebraic and superselection structure. It forces charged particles to be accompanied by "photon clouds" that cannot be realized…
This work revisits the classical concept of electric energy and suggests that the common definition is likely to generate large errors when dealing with nanostructures. For instance, deriving the electrostatic energy in semiconductors using…
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…