Related papers: Potential Momentum, Gauge Theory, and Electromagne…
We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields…
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called…
Both magnetic materials and light have always played a predominant role in information technologies, and continue to do so as we move into the realm of quantum technologies. In this course we review the basics of magnetism and quantum…
A description of electromagnetism as four-dimensional spacetime structure leads to the dynamics of a charged particle being determined only by the four-vector potential and the existence of an electromagnetic field depending on the…
The Lorentz force law of classical electrodynamics requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material. In contrast, the Einstein-Laub formulation does not invoke…
For an arbitrary electromagnetic field, we define a prepotential $S$, which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential…
There are three electromagnetic integrals of motion that can be interpreted as the energy. These are the background energy, the elastic energy and the integral in the torsion field commonly referred to as the energy of the electromagnetic…
We present a manifestly covariant formulation of relativistic electromagnetism, focusing on the computation of electromagnetic fields from moving charges in a manifestly Lorentz-covariant manner. The electromagnetic field at a given…
The Lorentz force equations provide a partial description of the geodesic motion of a charged particle on a four-manifold. Under the hypothesis that Maxwell's equations express symmetry properties of the Ricci tensor, the full…
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas…
The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon…
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…
In the first part of the present work, we focus on the theory of gravitoelectromagnetism (GEM), and we derive the full set of equations and constraints that the GEM scalar and vector potentials ought to satisfy. We discuss important aspects…
The gauge covariant derivative of a wave function is ubiquitous in gauge theory, and with associated gauge transformations it defines charged currents interacting with external fields, such as the Lorentz force exerted by an electromagnetic…
Textbooks play a fundamental role in teaching and learning in school science classrooms. In this paper we investigate the presentation of the nature of the electromagnetic field in a dozen of the world's most popular introductory university…
A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…
Separation of the spin and orbital angular momenta of the electromagnetic field has been discussed frequently in recent years. The spin and orbital angular momenta cannot be made simultaneously gauge invariant and Lorentz covariant and are…
A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…
The Maxwell's electromagnetic equations are isomorphic to the motion equation of a linear elastic continuum which is hard to compression though liable to shear deformation. The Coulomb gauge expresses the medium incompressibility. The…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…