Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. It has been shown that in the case of a beam with uniform phase space density the Vlasov-Maxwell equations can be replaced exactly by the hydrodynamic equations with a triple ...

We derive source-free Maxwell-like equations in flat spacetime for any helicity j by comparing the transformation properties of the 2(2j + 1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity j states that carry the irreducible representations of this group. The set of constraints so derived invol...

We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in [16], we propose an algorithm based on the use of bivariate B-splines spaces suitably adapted to electromagnetics. We construct B-splines spaces of variable interelement regularity on the parametric domain. These spaces (and their push-forwar...

The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the cognoscenti of differential forms on manifolds; namely, that charge conservation implies the inhomogeneous Maxwell equations. This is the reciprocal statement of one which is very well known among physicists: charge conservation, written in the...

The relation between the two most important in mathematical physics first order systems of partial differential equations is among those topics which attract attention because of their general, even philosophical significance but at the same time do not offer much for the solution of particular problems concerning physical models. The Maxwell equations can be represented in a Dirac like form in...

In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigate what is now known as the Maxwell-Dirac equivalence (MDE ) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ21ψ̃, wh...

In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigate what is now known as the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ21˜ψ, wh...

Following the technique of [1], we show that strictly static and strictly stationary solutions of the Einstein-Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field inherits the symmetry.

In this paper we discuss some unusual and unsuspected relations between Maxwell, Dirac and the Seiberg-Witten equations. First we investigate what is now known as the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ21˜ψ, wh...