 Null crossed electromagnetic field

Perpendicular fields with $\mathbf{E}\cdot \mathbf{B}=0$ and $E^2-c^2{B}^2=0$ form a null electromagnetic field. The constant-field Lorentz-force generator is nilpotent, so its exponential terminates as a polynomial.

Both invariants of the electromagnetic field tensor vanish for this field class.