Related papers: Electromagnetism: an intrinsic approach to Hadamar…
We derive one- and two-dimensional models for classical electromagnetism by making use of Hadamard's method of descent. Low-dimensional electromagnetism is conceived as a specialization of the higher dimensional one, in which the fields are…
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 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…
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…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
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…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
No positive result has been obtained on the magnetic monopoles search. This allows to consider different theoretical approaches as the proposed in this paper, developed in the framework of the Einstein General Relativity. The properties of…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a…
We propose a novel framework that interprets the electromagnetic field as a manifestation of spacetime pseudo-curvature, bridging electromagnetism with the geometric principles of general relativity. By introducing modified field equations,…
In order to analyse classical electromagnetism in a medium at finite temperature we introduce `an optical density operator', and reformulate Maxwell's equations with the operator, starting from the Dirac-equation-like formulation of…
In general relativity, Maxwell's equations are embedded in curved spacetime through the minimal prescription, but this could change if strong-gravity modifications are present. We show that with a nonminimal coupling between gravity and a…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and…
Despite the success of Maxwell's electromagnetism in the description of the electromagnetic interactions on small scales, we know very little about the behaviour of electromagnetic fields on cosmological distances. Thus, it has been…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…