Related papers: A New Formulation of Electrodynamics
A supersymmetric formulation of the classical action of interacting charged and neutral fermions with arbitrary anomalous magnetic moment is considered. This formulation generalizes the known action for scalar charged particles investigated…
Using Maxwell's mental imagery of a tube of fluid motion of an imaginary fluid, we derive his equations $\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, $\operatorname{curl} \mathbf{H} = \frac{\partial…
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…
In this lecture we discuss some interesting developments in the modern theory of electromagnetic field(s). In particular, by using the methods developed in Dirac's constraint dynamics we derive the Schr\"{o}dinger equation for the free…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
The Dirac approach to include magnetic charge in Maxwell's equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical…
In this paper after reviewing the Schouten and de Rham definition of impair and pair differential form fields (not to be confused with differential form fields of even and odd grades) we prove that in a relativistic spacetime it is possible…
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic…
We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
Conservation of energy and momentum in the classical theory of radiating electrons has been a challenging problem since its inception. We propose a formulation of classical electrodynamics in Hamiltonian form that satisfies the Maxwell…
The development of relational electromagnetism after Gauss appears to stop around 1870. Maxwell recognised relational electromagnetism as mathematically equivalent to his own formulae and called for an explanation of why so different…
Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
The generalized Maxwell equations with arbitrary gauge parameter are considered in the $11\times 11$-matrix form. The gauge invariance of such a model is broken due to the presence of a scalar field. The canonical and symmetrical Belinfante…
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has…
The electric and magnetic fields of a spatio-temporally varying electric current loop are calculated using the Jefimenko equations. The radiation and the nonradiation parts of the electromagnetic fields are derived in the framework of…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
The purpose of this course is to provide an introduction to Electromagnetic Theory. The foundations of electrodynamics starting from the nature of electrical force up to the level of Maxwell equations solutions are presented. It starts with…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…