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Null electromagnetic field

A null field has both electromagnetic invariants zero:

E \cdot B = 0, E^{2} = c^{2} B^{2} .

For a nonzero constant null field, the mixed tensor is nilpotent of index three,

F^{μ}_{ρ} F^{ρ}_{σ} F^{σ}_{ν} = 0.

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