Related papers: Generally Covariant Maxwell Theory for Media with …
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…
Generalized hydrodynamic theory, which does not rest on the requirement of a local equilibrium, is derived in the long-wave limit of a kinetic equation. The theory bridges the whole frequency range between the quasistatic (Navier-Stokes)…
We consider the associativity (or WDVV) equations in the form they appear in Seiberg-Witten theory and prove that they are covariant under generic electric-magnetic duality transformations. We discuss the consequences of this covariance…
In electrodynamics courses and textbooks the properties of plane electromagnetic waves in both conducting and non-conducting media are typically studied from the point of view of the prototype case of a monochromatic plane wave. In this…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the…
There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
Electromagnetic properties of a simple polarisable medium may be parameterised in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial (accelerating) frames and in the presence of…
An Electrodynamics solver for moving sources is introduced. The main challenges and formulation are highlighted. The solver enables the simulation of fields for sources undergoing arbitrary motion. Two examples of uniformly moving current…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
Maxwell's equations can be obtained in generalized coordinates by considering the electromagnetic field as an external agent. The work here presented shows how to obtain the electrodynamics for a charged particle in generalized coordinates…
We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in framework of Maxwellian theory, a novel convection displacement current is…
A hydrodynamic-type, macroscopic theory was set up recently to simultaneously account for dissipation and dispersion of electromagnetic field, in nonstationary condensed systems of nonlinear constitutive relations~\cite{JL}. Since it was…
The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from…
A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…