12 research outputs found
Magnetic Monopoles, Electric Neutrality and the Static Maxwell-Dirac Equations
We study the full Maxwell-Dirac equations: Dirac field with minimally coupled
electromagnetic field and Maxwell field with Dirac current as source. Our
particular interest is the static case in which the Dirac current is purely
time-like -- the "electron" is at rest in some Lorentz frame. In this case we
prove two theorems under rather general assumptions. Firstly, that if the
system is also stationary (time independent in some gauge) then the system as a
whole must have vanishing total charge, i.e. it must be electrically neutral.
In fact, the theorem only requires that the system be {\em asymptotically}
stationary and static. Secondly, we show, in the axially symmetric case, that
if there are external Coulomb fields then these must necessarily be
magnetically charged -- all Coulomb external sources are electrically charged
magnetic monopoles
Modeling Optical Properties of Liquid-Crystal Devices by Numerical Solution of Time-Harmonic Maxwell Equations
this paper, we discuss a method for solving a formulation in the frequency domain, i.e., for the time-harmonic form of the Maxwell equations. Such techniques have been used by numerical analysts in other setting