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### ME in Majorana algebras

The Majorana algebra denoted by  is defined as follows::

For the basis  in  we can take

where  are the PAULI matrices. Let
where  and . It can easily be seen that the basis elements  fulfil anticommutator relations. We now introduce the electro-magnetic field, which is given by the bivector
with . Hereby  is defined as the bivector
and  is just the vector . E and B are functions of the position  (GIBBS vector) and the time . Thus we have the coordinates
Now MAXWELL equations can be written in one single equation namely
where the right-hand side is the sum of the trivector  (charge density) and the vector  (current vector). We obtain
For the electric field yields now
Often one will have the field in the form of a vector potential . Then the equation
yields the relations
The latter relation is called LORENZ condition.

From the electro-magnetic field  one can also deduce other important quantities such as

For  follows
The coefficient of the first term reads energy density and the second one POYNTING vector. By scalar multiplication of  with  from the right we get the so-called MAXWELL stress tensor:
which had been introduced by M. RIESZ in 1947.

When we look for the flow of the energy momentum through a surface with as the unit vector of the normal at the point , then it is given by the energy momentum tensor

It is nothing other than as a vector valued linear function on the tangent space at each space point .

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