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We explore the possibility for generalized electromagnetism on flatspacetime. For a single copy of $U(1)$ gauge theory, we show that theGalileon-type generalization of electromagnetism is forbidden. Given that theequations of motion for the vector field are gauge invariant and Lorentzinvariant, 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 secondderivative of $A_\mu$.

A no-go theorem for generalized vector Galileons on flat spacetime