Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 37C / a

Withthe electromagnetic field tensor is the antisymmetric tensorUnder a Lorentz transformation $x^{\prime \mu }={\Lambda }^{\mu }{}_{\nu }{x}^{\nu }$, the four-potential transforms as a four-vector and thereforeThus $F$ is an antisymmetric rank-two tensor under Lorentz transformations.