Electromagnetic field invariants ($F_{\mu \nu }{F}^{\mu \nu },F_{\mu \nu }{\tilde{F}}^{\mu \nu }$)

For signature $(-,+,+,+)$ and a consistent orientation,Overall signs depend on tensor and orientation conventions, while their vanishing does not.

A null field has both electromagnetic invariants zero:For a nonzero constant null field, the mixed tensor is nilpotent of index three,