Related papers: Do we need to modify Maxwell's equations?
The manifestly Lorentz covariant Landau-Ginzburg equations coupled to Maxwell's equations are considered as a possible framework for the effective description of the interactions between low temperature superconductors and magnetic as well…
Using to a minimum extent special relativity input, and relying on the Lorentz-force expression for the force acting on a charged particle in motion under the influence of electric (E) and magnetic (B) fields, the Maxwell curl equations are…
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…
It has recently been proven that certain effective wavefunctions in fractional quantum mechanics and condensed matter do not have a locally conserved current; as a consequence, their coupling to the electromagnetic field leads to extended…
Although standard quantum mechanics has some non-local features, the probability current of the Schr\"odinger equation is locally conserved, and this allows minimal electromagnetic coupling. For some important extensions of the…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
The Maxwell vector potential and the Dirac spinor used to describe the classical theory of electrodynamics both have components which are considered to be ordinary smooth functions on space-time. We reformulate electrodynamics by adding an…
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,…
Though sufficient for local conservation of charge, we show that Maxwells displacement current is not necessary. An alternative to the Ampere Maxwell equation is exhibited and the alternative s electric and magnetic fields and scalar and…
It is shown that Einstein gravity tends to modify the electric and magnetic fields appreciably at distances of the order of the Compton wavelength. At that distance the gravitational field becomes spin dominated rather than mass dominated.…
It is well known that a covariant Lagrangian for relativistic charged particles can lead to a vanishing Hamiltonian. Alternatively, it is shown that using a "space+time" Lagrangian leads to a new canonical momentum and minimal coupling rule…
Using post-Galilean space and time derivatives transformations and quantum mechanics, we have found a new particle-wave equation besides the Klein-Gordon equation describing a spinless scalar particle. This new equation can also be obtained…
On transformation to the Fourier space $({\bf k}, \omega)$, the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations…
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, F --> F cos {\theta} + *F sin {\theta}. These transformations are indeed a symmetry of the theory in Noether sense. The…
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the…
A thoughtless treatment of Maxwell's equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and…
Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…