Definition
The electromagnetic tensor can be defined using the electromagnetic four-potential:
and its covariant form is found by multiplying by the Minkowski metric η of signature (+,−,−,−) :
where A is the vector potential, ϕ is the scalar potential and c is the speed of light.
The Electric and magnetic fields can be expressed in terms of A and ϕ by:
By definition, the electromagnetic tensor is the exterior derivative of the differential 1-form :
therefore F is a differential 2-form on spacetime. In an inertial frame, the matrices of F read:
and by lowering indices
Read more about this topic: Electromagnetic Tensor
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