  We explore the possibility for generalized electromagnetism on flat
spacetime. For a single copy of $U(1)$ gauge theory, we show that the
Galileon-type generalization of electromagnetism is forbidden. Given that the
equations of motion for the vector field are gauge invariant and Lorentz
invariant, follow from an action and contain no more than second derivative on
$A_\mu$, the equations of motion are at most linear with respect to second
derivative of $A_\mu$.
