The electromagnetic tensor has an electromagnetic four-potential field possessing gauge symmetry.
2.
The contravariant electromagnetic tensor in the ( + " " " ) signature is given by
3.
As a whole it is the electromagnetic tensor expressed more compactly as a bivector, and is used as follows.
4.
Where is the bivector form of the electromagnetic tensor, is the four-current and is a suitable differential operator.
5.
Formally, special relativity combines the electric and magnetic fields into a rank-2 tensor, called the " electromagnetic tensor ".
6.
The transformations in this form can be made more compact by introducing the electromagnetic tensor ( defined below ), which is a covariant tensor.
7.
Using the four potential instead of the electromagnetic tensor has the advantage of being much simpler and it can be easily modified to work with quantum mechanics.
8.
Gauss's law for magnetism and the Faraday Maxwell law can be grouped together since the equations are homogeneous, and be seen as electromagnetic tensor.
9.
The Pl�cker coordinates are bivectors in ! 4 while the electromagnetic tensor discussed in the previous section is a bivector in ! 3, 1.
10.
A second approach is to combine them in a single object, the six-dimensional electromagnetic tensor, a tensor or bivector valued representation of the electromagnetic field.
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