Nächste Seite:ME in Majorana algebrasAufwärts:Maxwell equations (ME)Vorherige Seite:Classical formulation

ME with magnetic monopols

In consideration of magnetic monopols we have the following models:

1. Vectorial form:

\begin{eqnarray*}&&\nabla\times E+\frac{1}{c}\partial _t\;B=-\frac{4\pi}{c}j',\......x]&&\nabla\cdot E=4\pi\rho,\\ [2ex]&&\nabla\cdot B=4\pi \rho'.\end{eqnarray*}
Here $j,j'$ are the electric or monopole current density.

2. (with complex vector $W=E+{\bf i}B$):

\begin{eqnarray*}&&\nabla \times -\frac{\bf i}{c}\partial _t\; W=\frac{4\pi {\b......j'+{\bf i} j),\\ [2ex]&&\nabla \cdot W=4\pi(\rho+{\bf i}\rho').\end{eqnarray*}

3. Ohmara equations $(x_0=ct)$:

\begin{eqnarray*}&&\nabla\times E+\partial _{x_0}\;B=j +\nabla h,\\ [2ex]&&\na......ial _{x_0}e,\\ [2ex]&&\nabla\cdot B=-\sigma +\partial _{x_0} h.\end{eqnarray*}
where $e$ is the scalar field and $h$ is a pseudo-scalar field, $\rho , i$ and $\sigma , j$ are the density and current of electric and magnetic charge, respectively of the magnetic pole.

A late reference: V. Majernik, (1999) Quaternionic formulation of the classical fields, Advances in Applied Clifford Algebras, 9 No. 1, 119-130.

collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg