Related papers: Generalized Maxwell equations for exterior-algebra…
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be…
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,…
Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants.…
Electromagnetic force and torque are typically derived from a stress tensor in conjunction with Maxwell's equations of classical electrodynamics. In some instances, the Principle of Least Action (built around a Lagrangian) can be used to…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in $N$-dimensions that follows from an action principle. Further, we show that our $N$-dimensional…
For the fermion field in the two-dimensional Gross--Neveu model, we introduce a flow equation that allows a simple $1/N$ expansion. By employing the $1/N$ expansion, we examine the validity of a universal formula for the energy--momentum…
We quantize the massless p-form field that obeys the generalized Maxwell field equations in curved spacetimes of dimension n > 1. We begin by showing that the classical Cauchy problem of the generalized Maxwell field is well posed and that…
We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can…
Charges are everywhere because most atoms are charged. Chemical bonds are formed by electrons with their charge. Charges move and interact according to Maxwell's equations in space and in atoms where the equations of electrodynamics are…
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
In this paper, we apply the generalized integration constants method in field theory to quantize Maxwell and the Klein-Gordon free fields. The study is performed in both position and momentum spaces, to obtain equal-time Dirac brackets…
We present a class of solutions to the Einstein-Maxwell equations in d-dimensions, all of which are asymptotically (anti)-de Sitter space-times. They describe electrically charged rotating solutions, which are generalizations of those found…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
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,…
Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their…
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…
By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schr\"odinger equation and the equations of continuum mechanics. A generalized Maxwell distribution has been used as the…